With the rapid development of integrated photonics, expensive and bulky commercial spectrometers force people to make more efforts to investigate high-performance, integrated and low-cost spectrometers. Spectrometers benefiting from the complementary metal-oxide semiconductor (CMOS) technology have greatly enriched the applications of spectrum detection while devices based on optical fibers still have potential development room. Owing to the strong dependence of multimode interference on wavelength generated in a multimode fiber, probe signals of arbitrary spectra could be detected by a detector array integrated on the top and reconstructed by using a compressive sensing (CS) algorithm. The CS algorithm has been widely used in signal processing, which saves more computing storage and time but maintains the same precision. With the interference pattern system, our spectrometer based on a fiber taper achieves a spectral resolution of 20 pm (one order of magnitude better than commercial spectrometers) and a detection bandwidth of more than 200 nm on a device length of 1 mm. After optimizing the energy function, the spectral reconstruction results show excellent detection capability and metamerism effect superior to RGB cameras or human eyes, providing a significant role for portable multi-functional on-chip systems in future.