An integrator is quite a suitable active element for high-speed filters. The effect of its excess phase shifts, however, is severe in the case of high-Q filter realization. The deterioration due to the excess phase shifts cannot be avoided when only integrators are used as frequency-dependent elements like in leapfrog realization. This paper describes a design of second-order high-speed and high-Q filters with low sensitivity to excess phase shifts of integrators by adding a passive RC circuit. The proposed method can drastically reduce the effect due to the undesirable pole of an integrator, which is the cause of the excess phase shifts, compared to conventional filters using only integrators. As an example, a fourth-order bandpass filter with 5-MHz center frequency and Q=25 is implemented by the proposed method on a monolithic chip. The results obtained here show quite good agreement with the theoretical values. This demonstrates effectiveness of the proposed method and feasibility of high-speed and high-Q filters on a monolithic chip.