Waqas Khan, now aged 23, hit Hassan Ali on the night of January 28, 2015 as the latter man crossed Staniforth Road in Darnall, Sheffield, after coming out of a takeaway.
Mr Ali never regained consciousness and died in hospital on February 6.
Khan, who is accused of causing death by careless driving, said he had been looking to the right at an upcoming junction.
The accounting and financial management student at Sheffield University said he had been trying to be 'extra careful' as he drove home in snowy weather from revising at university for an exam the following day.
The court heard Khan had passed his driving test at the fifth attempt in June 2014.
He said he did not see Mr Ali on the left hand side of the road and was began looking ahead to the right at a junction ahead to see if there would be any vehicles coming out.
"I made sure I was extremely careful and cautious and to be extra wary of my surroundings and potential hazards like cars pulling out from a junction."
He said he had been looking to the right for a "few seconds".
"I couldn't see properly. I wanted to be careful a car wasn't coming from there. Because of the weather conditions it took me a bit longer than it would have usually."
Khan accepted that CCTV showed his car driving over the white line in the middle of the road before he hit Mr Ali and said he had not been aware of it happening.
"I wasn't looking straight at the time, I was focused on the junction.
"As soon as I put my eyes back on the road, he was just there in front of me."
He said he put his brakes on, flung open his car door and ran to the injured man, realising at that point he knew who the pedestrian was. Khan said he held Mr Ali in his arms as he waited for an ambulance to arrive.
Cross-examining, Richard Thyne told Khan the prosecution case against him was that he should have been focused on the road in front of him.
Khan said: "I believe in my circumstances I was trying to be careful. If the weather wasn't so bad, I wouldn't have spent so much time with my eyes not on the road."
The jury has now retired to consider its verdict. The case continues.