The purpose of this paper is to study the partial functional linear regression model with a random missing response and measurement errors in explanatory variables.The estimators of unknown parameters and unknown coefficient functions in the model and their asymptotic properties are discussed, respectively. Firstly, the missing data and the data with measurement errors are processed by some data preprocessing method, as well as the model is transformed into a general functional linear regression model. Then the empirical form of the model is given by Karhumen-Loeve expansion (K-L expansion) and principal component analysis. Finally, the least squares estimates of the corresponding unknown variables are obtained by minimizing the objective function with classical multivariate statistical analysis, and the asymptotic normality of the parameter estimators is proved under certain conditions. The convergence rate of the estimator of function and slope function shows that the estimators given are effective estimators, and the statistical inference method of functional data under complete observation is extended to the case of incomplete observation under certain conditions.