The maximum correntropy criterion (MCC) algorithm with constant kernel width leads to a tradeoff problem in terms of convergence rate and steady-state misalignment. Thus, this brief proposes a variable kernel width (VKW) MCC algorithm to overcome this problem. The optimal kernel width of the proposed VKW-MCC algorithm is calculated at each iteration by maximizing exp(-e_k²/2σ_k²) with respect to the kernel width σ_k, wherein the kernel width is a function of the error, to make the error with greatest attenuation along the direction of the gradient ascent. Simulations in the contexts of system identification and echo cancellation have demonstrated that the proposed VKW-MCC algorithm yields a superior performance.