This letter proposes a new algorithm for Gaussian process classification based on posterior linearization (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearization of the conditional mean of the labels and accounting for the linearization error. PL has some theoretical advantages over expectation propagation (EP): all calculated covariance matrices are positive definite and there is a local convergence theorem. In experimental data, PL has better performance than EP with the noisy threshold likelihood and the parallel implementation of the algorithms.