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This paper presents a new design of a hat-fed reflector antenna for satellite communication, where low sidelobe and cross polar levels are required over a wideband. The hat feed has been optimized in the design by using the genetic algorithm (GA) through a commercial FDTD solver QuickWave V2D together with own developed Matlab code. The Gaussian vertex plate has been applied at the centre of the reflector for improving the reflection coefficient of the whole hat-fed reflector antenna. A return loss of 15 dB is obtained over a bandwidth of 47.5%. The simulations have been verified by measurements; both of them are presented in the paper.