Nonlinear processes and non-Gaussian properties are challenging subjects for soft sensor modeling of chemical processes. In this paper, we propose a D-vine copula regression method based on a Hamiltonian Monte Carlo (HMC) sampling strategy (HMCCR). In the data pretreatment process, the rolling pin monotonic transformation method is used to ensure that the data have a monotonic relationship. Subsequently, a D-vine copula model is established to obtain the conditional probability density of the key variables based on the auxiliary variables. The expected value, the variance, and the prediction uncertainty of the query data set are calculated using the HMC method. The proposed regression method can successfully approximate the nonlinear and non-Gaussian relationship between the output and input variables using the vine copula function. In addition, we also propose a supplementary sampling strategy based on the HMCCR model to remind operators to supplement the manual analysis. The validity and performance of the proposed method are demonstrated using two industrial examples.