Kamel, when the surging occurs, is the engine speed varying to match the mower's speed? If it is, I doubt the cause is the transmission - it is more likely to be that the engine hunts under load. Hunting by a governed engine has one of two causes: friction/jamming in the governor linkage, or lean mixture. Lean mixture is by far the more common cause.
I suggest you post pictures of your mower, and details of the engine. I am guessing it is a Briggs & Stratton, but we need the model, type and code numbers which are stamped on the cooling air cowl. Then we can get specific about how to deal with this.
