Hybrid Bayesian Networks (HBNs), which contain both discrete and continuous variables, arise naturally in many application areas (e.g., artificial intelligence, data fusion, medical diagnosis, fraud detection, etc). This paper concerns inference in an important subclass of HBNs, the conditional Gaussian (CG) networks. Inference in CG networks can be NP-hard even for special-case structures, such as poly-trees, where inference in discrete Bayesian networks can be performed in polynomial time. This paper presents an extension to the Hybrid Message Passing inference algorithm for general CG networks (i.e., networks with loops and many discrete parents). The extended algorithm uses Gaussian mixture reduction to prevent an exponential increase in the number of Gaussian mixture components. Experimental results compare performance of the new algorithm with existing algorithms.