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Adaptive filtering for complex data has received more attentions recently. As a similarity measure for the complex random variables, complex correntropy has been shown robustness in the design of adaptive filter. However, existing works using complex correntropy are limited to a Gaussian kernel function, which is not always the optimal choice. In this paper, we propose a class of new adaptive filtering algorithm for complex data using complex correntropy, which employs the complex generalized Gaussian density function as kernel function. Stability analysis provides the bound for learning rate and the steady-state excess mean square error is derived for theoretical analysis. Simulation results show that the proposed algorithm has zero probability of divergence and verify its superiority.