This paper proposes a general formalism for evaluating hybrid Bayesian networks. The formalism approximates a hybrid Bayesian network into the form, called fuzzy partial least-squares Bayesian network (FPBN). The form replaces each continuous variable whose descendants include discrete variables by a partner discrete variable and adding a directed link from that partner discrete variable to the continuous one. The partner discrete variable is acquired by the discretization of the original continuous variable with a fuzzification algorithm based on the structure adaptive-tuning neural network model. In addition, the dependence between the partner discrete variable and the original continuous variable is approximated by fuzzy sets, and the dependence between a continuous variable and its continuous and discrete parents is approximated by a conditional Gaussian regression (CGR) distribution in which partial least-squares (PLS) is proposed as an alternative method for computing the vector of regression parameter. The experimental results are included to demonstrate the performances of the new approach.