Learning a low-dimensional image representation yields effective and efficient face recognition. The use of such a representation helps to weaken the curse of dimensionality. However, the traditional facial representation method is not robust against partial occlusions or variations of expression. To solve this problem, this paper proposes a more reliable, complex-valued representation of facial image. The robust representation is based on the proposed locality-preserving complex-valued Gaussian process latent variable model (LP-CGPLVM). In the LP-CGPLVM, the Euler formula is utilized to transform original facial images into the complex domain. A proper complex GP is employed to model the mapping between the complex-valued high-dimensional data and the corresponding low-dimensional representation. Moreover, the locality-preserving constraint is taken into consideration to preserve the neighborhood data structure. The experimental results indicate that our proposed method is robust against partial occlusions and various facial expressions.