Self-triggered control is a control method that the control input and the sampling period are computed simultaneously in sampled-data control systems, and is studied in the field of networked control systems. In this paper, a new approach for self-triggered control is proposed based on the model predictive control (MPC) method. First, self-triggered MPC with delay compensation in which the delay-compensation input is introduced is newly formulated. Next, in order to efficiently solve this MPC problem, the optimal control problem with horizon one is formulated, and an approximate solution method is derived. Finally, the effectiveness of the proposed approach is shown by a numerical example.