The 1939 aircraft prototype engineering plan provided for development of fighters with liquid-cooled engines, with a flight speed of 620-650kph. The task was given to a number of design teams, including design department No 15 of plant No 165 headed by P.O. Sukhoi. The performance requirements (PR) of the Air Forces, for a single-seat fighter with engine cannon M-103P and turbo compressor (TC) or M-103S with two-speed supercharger, were finalised in November-December 1938 and approved by AFRA Chief of Bureau A.D. Loktionov on 8th March 1939. By that time, the Design Bureau of V.Ya. Klimov had already started full-scale work to produce a boosted engine, the M-105. On 23rd May 1939, P.O. Sukhoi presented a conceptual design of a fighter with the M-105P engine, which was accepted and approved on 1st June, with the aeroplane mock-up approved on 26th July. A 29th July Resolution of the USSR CPC Defence Committee approved an aircraft prototype engineering plan. The Resolution, called “On Development of New Prototype Fighter Aeroplanes in 1939-40,” committed Chief Designer P.O. Sukhoi and director of plant No 135 Neishtadt to designing and producing two single-seat cannon-armed fighters to be submitted for governmental testing in March and July 1940 respectively. The aeroplane was designed as a medium-altitude fighter. It could not be regarded as a high-altitude aircraft since the cockpit was not to be pressurized. High-ceiling capability was engineered using two TC-2 turbo compressors and a number of other design solutions. Interestingly, despite the explicit requirement (in accordance with the DC resolution) to use turbo compressors to raise the ceiling, a majority of designers came to oppose it as the studies of new fighter designs progressed, with P.O. Sukhoi continuing the efforts to develop a high-performance medium-altitude fighter in spite of this. To facilitate refinement of the fighter's powerplant, the bureau built a special test bed.
The first prototype aeroplane, I-135, (since December 1940 known as the Su-1) was completed at Kharkov plant No 135 on 25th May 1940 and sent by railway to CAHI for manufacturer's flight tests. On 15th June, pilot A.P. Chernavsky performed the aeroplane's first flight. The testing continued till 3rd August when A.P. Chernavsky made the mistake of landing the I-135 with its landing gear retracted, the aeroplane suffering minor damage as a result. The repairs completed, the I-135's testing resumed in mid-September, with pilot P.M. Popelnyushenko at the controls. Shortly thereafter, however, on 2nd October, the engine broke up in mid-flight. This time, the flight was brought to a successful conclusion, the pilot succeeding in landing the aeroplane. The engine replaced, the flights resumed on 10th November with V.P. Fyodorov at the controls as P.M. Popelnyushenko had been put on sick leave. The tests continued till late April 1941, with the aeroplane's basic flight performance having been evaluated, but with the powerplant failing to be fine-tuned as a result of the TC-2's frequent breakdowns. And without its turbo compressors in place, the Su-1 did not have much to offer compared to A.S. Yakovlev's I-26, which had already been put into production.
It was already under the supervision of P.D. Grushin that the second I-135 was nearing completion at plant No 135 when in January 1941 it was sent, not yet completed, to plant No 289, where the aeroplane, subsequently referred to as the Su-3, was finally completed. The plane was never tested. A 16th April Resolution of the USSR CPC and CC RCP (b) put a stop to work on the aircraft Su-1 and Su-3 "…due to the established futility of further design, engineering and testing efforts…". There is no reliable information as to what happened to them after that. Some data indicate that the Su-1 was destroyed during bombardment of the train it was on on its way to Novosibirsk, and the Su-3 was at the MAI FRI in Novosibirsk. In 1943, there was an attempt undertaken to use it for testing turbo compressors.