Maximum correntropy criterion (MCC) has been widely used in Kalman filter to cope with heavy-tailed measurement noises. However, its performance on mitigating non-Gaussian process noises and unknown disturbance is rarely explored. In this letter, we extend the definition of correntropy from a single kernel to multiple kernels. Then, we derive a multi-kernel maximum correntropy Kalman filter (MKMCKF) to cope with multivariate non-Gaussian noises and disturbance. Three examples are provided to show the effectiveness of the proposed methods.