This paper investigates the moving horizon estimation (MHE) problem for process systems with multi-rate sampling and bounded noises, where the sampling rates of the sensors are not identical. In the sense of the multi-rate systems, some sensors may have no measurements at certain sampling times, which can be regarded as measurement missing and may significantly degrade the estimation performance. The main purpose of this paper is to design an estimator by using a multi-rate MHE (MMHE) strategy. A binary switching sequence is introduced to model the multi-rate sampling, and the missing sample of the slow measurement is compensated by a prediction value. By choosing a cost function, the optimal estimator is obtained by solving a regularized least-squares problem. The stability analysis for the optimal estimator is also presented. Finally, a continuous stirred tank reactor (CSTR) example is given to demonstrate the effectiveness of the proposed method.