In this paper, we present a control method for the control plant subject to the constraint on the power spectral density of the control input. The constraint condition on the power spectral density is defined using the periodogram. This constraint is represented as a quadratic inequality on the combination of the control inputs of the adjacent several time steps. To constrain the power spectral density of the control input, the finite impulse response filter is connected to the input channel of control plant and the constrained model predictive controller is used. The filter is designed so that when it receives the amplitude-constrained signal its output signal satisfies the constraint on the power spectral density. The model predictive controller with the amplitude-constrained output controls the augmented plant which consists of the control plant and the filter. Numerical simulations verify the effectiveness of the proposed method.