Latent class analysis (LCA) can be extended to latent class regression (LCR) model after including the effect of covariates. In general, parameter estimates in latent class regression model is more accurate than latent class analysis due to the covariates, i.e., the parameters are estimated with more precise confidence intervals. Many studies have discussed various methods to handle missing data in latent class analysis, but there is little research on missing data in latent class regression models. This study examined the effect of sample sizes, latent class proportions, conditional probabilities, missing data rates of major and minor missing variables on parameter estimations. We are particularly interested in monotone missing data, and compared the performance of discriminant function imputation and logistic regression imputation. We also investigated the impact of the factors on the accuracy of parameter estimation under different combinations. The result showed that with larger sample size, lower missing data rates of the major missing variables, y4, and equal latent class proportions, the parameter estimation are more accurate. The influence of the minor missing variables y3 is not significant. Latent class conditional probability has an inverse effect on parameter estimation, i.e., the larger difference of the conditional probabilities, the smaller the bias. Imputation method has some differential effect on conditional probability, but not on latent class proportions. The bias is higher for discriminant function imputation than logistic regression imputation.