<p>We propose a hybrid complex spectral conjugate gradient algorithm with an adaptive complex-valued stepsize (HCSCGACS) for training complex-valued neural networks. The algorithm introduces a complex-valued stepsize updating criterion to address the issue of the complex-valued stepsize not satisfying the generalized inexact line search conditions, ensuring that the new training direction always maintains the descent property. This feature enables the algorithm to extend the search range from half-line to half-plane, thereby avoiding saddle points more efficiently. Furthermore, we provide a theoretical analysis of HCSCGACS, demonstrating its convergence under appropriate conditions and verifying its descent property during training. Experimental results show that HCSCGACS outperforms multiple state-of-the-art algorithms in terms of convergence speed and training accuracy, significantly improving the overall training efficiency.</p>