A robust successive interference cancellation (SIC) receiver is designed to work in an impulsive noise environment. The channel includes additive noise which may contain impulsive elements that affect the ranking and detection of each user. The traditional SIC scheme uses linear correlation and its performance deteriorates in non-Gaussian noise. In the proposed receiver, a robust nonlinearity is introduced which effectively clips out the outliers. Parameter estimation is carried out using the output of a bank of robust correlators and the receiver effectively cancels interferences in the order of received signal powers. The results indicate that the proposed robust SIC receiver provides superior performance to the conventional one in terms of bit error rate. The improvement in performance persists for asynchronous reception, as well as power imbalance among users.