In this paper, a set of birefringent element measurement systems is constructed based on the principle of laser feedback and measures the phase delay of the birefringent element, which is a 1/4 wave plate widely used in the optical system. The temperature frequency stabilization method was introduced into the system's He-Ne laser light source to improve further the stability of the system. The temperature of the laser cavity was controlled by changing the cavity length, thereby making the laser work steadily in the single longitudinal mode for a long time. Moreover, this frequency stabilization method attained a frequency stability of 10^-7 for the He-Ne laser, thus meeting the laser feedback measurement requirements. The phase delay of the 1/4 wave plate was measured herein for 10 times in two different ways, unsteadiness and temperature stabilization, using the same system. The experimental results show that the maximum deviation of the 10 repeated system measurements without frequency stabilization is 1.29° and the standard deviation is 0.47°. In contrast, the maximum deviation of 10 repeated measurements reduces to 0.83° and the standard deviation to 0.29° after the temperature stabilization. Hence, it is concluded that the stability of the system greatly improves with frequency stabilization.