All-solid-state continuous-wave (CW) single-frequency tunable Ti:sapphire (Ti:S) laser is an important source in quantum optics and atomic physics. However, intracavity etalon (IE) locking is easily influenced by the intensity noise of the pump source in the low frequency band. In order to address this issue, a differential detector with dual-photodiodes (PDs) is designed and employed in the experiment. Both PDs are used to detect the lights of the pump source and the built Ti:S laser, respectively. As a result, the influence of the intensity noise of the pump source on the stability of the IE locking is successfully eliminated and the IE is stably locked to the oscillating longitudinal-mode of the laser. On this basis, a stable CW single-frequency tunable Ti:S laser is realized. The presented method is beneficial to attain a stable single-frequency tunable laser with immunity to the intensity noise of the pump source.