In this article, was formulated and solved the optimal control problem with two bounded controls using the Pontryagin maximum principle. A controlled model of CAR T-cell immunotherapy, which describes the dynamics of CAR T-cells, normal or healthy B-cells, cancer cells and cytokines as four ordinary differential equations of the Lotka-Volterra type with two bounded controls. The first is the concentration of injected CAR immune T cells and its effect on system parameters. The second reflects the effect of an immunosuppressant such as tocilizumab and its role in preventing cytokine storms. The authors formulate an optimal control problem to minimize tumor cells and cytokine concentration. Then the Pontryagin maximum principle is applied and the type of optimal controls depending on the switching functions is found. It is revealed that the second optimal control, reflecting the suppressive effect of a possible “cytokine storm”, is constant, taking the maximum value over the entire time interval of the treatment period. Analytically examining the properties of the first switching function, the authors find that the corresponding optimal control takes a maximum value at the end of the time interval. Therefore, the type of the switching function is found, which determines the behavior of the first optimal control responsible for the injection schedule CAR. It turned out that this function has no more than two switches, and that, depending on the parameters of the model, it can accept one of five optimal treatment scenarios. Thus, a controlled model of CAR T-cell immunotherapy was created and the problem of its optimal control was solved.