This study proposes a new design for generalized predictive control in a multirate system in which the sampling interval of the plant output is an integer multiple of the hold interval of the control input. We design a system with one degree of freedom, and then, for integral action we extend it to two degrees of freedom. Because the integral compensation is revealed only when a modeling error or a disturbance arises, the integral compensation does not cause the transient response to deteriorate when these are absent. Moreover, even if there is a modeling error or a step-type disturbance, the plant output converges to the step-type reference input, because the integral compensation is revealed. The proposed design is based on a state-space representation, and hence it can be easily extended to a multivariate system.