Correntropy, a novel localized similarity measure defined in kernel space, has been successfully used as a cost function in adaptive system training. The adaptive algorithms under the maximum correntropy criterion (MCC) have been shown to be robust to impulsive non-Gaussian noises. However, they may converge slowly especially at a region far from the optimal solution. In this paper, we propose a new MCC algorithm with a variable step-size (VSS) called the VSS-MCC algorithm, which may achieve a much faster convergence speed while maintaining similar steady-state performance. In the new algorithm, the step-size is updated based on an approximation for the curvature of performance surface. Simulation results demonstrate the superior performance of VSS-MCC compared with the original MCC algorithm.