Is it normal for a person particularly male who does strength training or workout and eat a good diet to gain muscle and at the same time gain fat at the first few months of training?

If you are NOT experiencing fat gains you are most likely not eating enough to support muscle growth.

When gaining muscle to have to have excess calories in your diet. These calories are used to repair muscles and create larger muscle cells. These excess calories should come from a balance of carbs, proteins, and fats.

however when gaining muscle your body cannot use EVERY calorie towards muscle gain so some will be stored as fat.

I myself am on a "bulking stage" and i eat everything in sight, besides sweets. I eat anywhere from 3200-4000 calories a day.

Make sure to have a high carb/ high protein shake after workouts to speed recovery between workouts :).