Gather all your ingredients.

In a medium saucepan, mix together sugar, flour, and salt. Add the eggs, stirring thoroughly. Pour in the milk and cook over low heat, stirring constantly.

Once the mixture thickens enough to coat the back of a metal spoon, remove it from the heat. Continue stirring briefly to cool it slightly. Mix in butter and vanilla until the pudding becomes smooth.

In a serving dish, alternate layers of pudding, banana slices, and vanilla wafers.

Refrigerate for at least 1 hour before serving.