We propose and demonstrate a low-cost and simple fiber optic cantilever accelerometer with a spherical tip based on Gaussian beam focusing. The accelerometer consists of ceramic ferrule, ceramic sleeve, receiving fiber and emitting fiber, where both fibers are single mode fiber, the ferrule and sleeve have characteristics of high precision, which reduce the difficulty of optical alignment. The end of the emitting fiber is made into a spherical tip for focusing the Gaussian beam to improve sensitivity. When the accelerometer is in operation, the emitting fiber acts as a cantilever beam, the acceleration can be measured by detecting the transmission power. Further, our experimental results show that the spherical fiber tip can improve the acceleration sensitivity by 67% over 10 Hz-1000 Hz without reducing the working bandwidth. In addition, it is found that the fiber accelerometer has a high signal-to-noise ratio (SNR) up to 60 dB, and a low harmonic distortion of better than -30 dB, rendering a quasi-8-shaped directionality at the working frequency ranging from 10 Hz to 1200 Hz. This clever sensor structure may have potentials for developing high-performance and cost-effective accelerometers and hydrophones.