Given that the periods of slow sampling output channels are not synchronous with the reference period, the model predictive control algorithm is inapplicable to the multi-rate system. To solve this problem, we propose a model identification and model predictive control strategy applied to the multi-rate system. First, in accordance with the different numbers of sampling points in the steady-state time, we propose two methods to establish the unit step response model. Second, we present a model predictive control strategy to solve the asynchronicity of the control periods of the slow sampling output channels with the reference period. A characteristic of the control strategy is that the actual output value is predicted by the model predictive value of each reference period and the actual forecast error is used to correct the output forecast value. Finally, the control strategy is applied to a typical heavy oil distillation column system. The validity and the application range of the control strategy are verified by setting various slow sampling periods and model mismatch degrees.