A directionally discriminable curvature sensor based on a chirped fiber Bragg grating Fabry–Perot interferometer (CFBG-FPI) is proposed and demonstrated by staggering two CFBGs in parallel in the fiber core with femtosecond laser point-by-point technology. The experimental results show that the light intensity of the interference dip tends to become stronger and weaker in two opposite bending directions, respectively, with a maximum sensitivity of 4.93 dB/m⁻¹. This sensor has a temperature sensitivity of 2.31 × 10⁻⁴ dB/°C resulting in a cross-sensitivity as low as approximately 4.7 × 10⁻⁵ m⁻¹/°C. The sensor is simple to manufacture, compact, and can be cascaded by multiple sensors to achieve multi-point detection, which is expected to play an important application in structural health detection.