Because the posterior probability of the latent function needs to be approximated by a tractable Gaussian function, the traditional Gaussian process classification algorithms usually suffer from high computational cost. Therefore, a new Gaussian process classification algorithm is proposed. The basic idea is to use Parzen-window method to estimate the posterior probability of training data, and then transform the classification problem to a regression problem based on the obtained posterior probability. As a result, the explicit expression of the posterior probability of the latent function can be derived analytically and the high computational cost caused by approximating the posterior probability with Gaussian distribution is also avoided. The experimental results show that the proposed algorithm can achieve superior classification accuracy to the existing Gaussian process classification algorithms.