A Gaussian Process makes prediction based on the existing observed data. But in many cases, information is not limited to observations. Extra information, such as physical constraints and empirical knowledge, exists in many engineering problems. This paper presents a Bayesian-Entropy method to encode constraints into a Semiparametric Gaussian Process. The Bayesian-Entropy method can encode various types of constraints by adding an additional term to the Bayesian equation. The Bayesian-Entropy regression method can incorporate values and derivative information into the classical Bayesian regression as constraint. By adjusting the mean function in Semiparametric Gaussian Process according to the Bayesian-Entropy regression principle, extra information, such as the expected value and/or the derivative at a specific point, can be encoded into the regression function. Comparing with the traditional method, the constrained Semiparametric Gaussian Process benefits from the available extra information and can make better prediction outside the range of training data.