The System identification explores ways to obtain mathematical models of an unknown system. However, as a result from the intrinsic random nature of system or from the environment noise, it is very hard to find a perfect mathematical representation of a real system. This paper aims to evaluate the Maximum Correntropy Criterion (MCC) performance using the gradient descent and the Fixed-Point. Both methods were compared in different noise scenarios and their behavior with different system models. The importance of the free parameters was also studied on both methods. The results show that the fixed-point has a better performance and are less noise sensitive.