A simple, spectral-drift-insensitive interrogation scheme for a multicore fiber Bragg grating (FBG)-based directional curvature sensor is proposed. The basic principle is to transform the wavelength shift of FBGs into the reflected power variation, which is accomplished by utilizing a broadband source with a sinusoidal spectrum. The closed-form expression of the relationship between the reflected power of the FBG and the corresponding peak wavelength is derived for the first time, to the best of our knowledge; therefore, the peak wavelength of the FBG can be precisely interrogated by using a single photodiode. The experimental results show that, with respect to conventional wavelength measurement by an optical spectrum analyzer, the demodulated wavelength error by our proposed interrogation scheme is within ±20 pm. The proposed scheme is further extended to interrogate the direction and curvature using a multicore FBG-based curvature sensor; the interrogated curvature with an error less than 8% is achieved.