Soft labels allow a pattern to belong to multiple classes with different degrees. In many real world applications the association of a pattern to multiple classes is more realistic; to describe overlap and uncertainties in class belongingness. The objective of this work is to develop a fuzzy Gaussian process model for classification of soft labeled data. Gaussian process models have gained popularity in the recent years in classification and regression problems and are example of a flexible, probabilistic, non-parametric model with uncertainty predictions. Here we derive a fuzzy Gaussian model for a two class problem and then explain how this can be extended to multiple classes. The derived model is tested on different fuzzified datasets to show that it can adopt to various classification problems. Results reveal that our model outperforms the fuzzy K-Nearest Neighbor (FKNN), applied on the fuzzified dataset, as well as the Gaussian process and the K-Nearest Neighbor models used with crisp labels.