A bootstrapped analog switch with constant on-resistance is proposed for the successive approximation (SA) analog-to-digital converters (ADCs) that have many input-sampling switches. The initialization circuit, which is composed of a short pulse generator and a transmission gate, improves the linearity of the proposed bootstrapped analog switch by reducing the effect of the capacitive load. To evaluate the proposed bootstrapped analog switch, the 10-bit 1MS/s CMOS SA ADC with a rail-to-rail differential input signal was designed by using a 0.18µm CMOS process with 1.0V supply voltage. The proposed bootstrapped analog switch reduced the maximum V_GS variation of the conventional bootstrapped analog switch by 67%. It also enhanced the signal to noise-distortion ratio of the SA ADC by 4.8dB when the capacitance of its gate node is 100fF, and this improvement was maximized when the capacitance of its gate node increases.