Multiview learning reveals the latent correlation among different modalities and utilizes the complementary information to achieve a better performance in many applications. In this paper, we propose a novel multiview learning model based on the Gaussian process latent variable model (GPLVM) to learn a set of nonlinear and nonparametric mapping functions and obtain a shared latent variable in the manifold space. Different from the previous work on the GPLVM, the proposed shared autoencoder Gaussian process (SAGP) latent variable model assumes that there is an additional mapping from the observed data to the shared manifold space. Due to the introduction of the autoencoder framework, both nonlinear projections from and to the observation are considered simultaneously. Additionally, instead of fully connecting used in the conventional autoencoder, the SAGP achieves the mappings utilizing the GP, which remarkably reduces the number of estimated parameters and avoids the phenomenon of overfitting. To make the proposed method adaptive for classification, a discriminative regularization is embedded into the proposed method. In the optimization process, an efficient algorithm based on the alternating direction method and gradient decent techniques is designed to solve the encoder and decoder parts alternatively. Experimental results on three real-world data sets substantiate the effectiveness and superiority of the proposed approach as compared with the state of the art.