Metamaterials with multiband optical perfect absorption effect are highly desired in applications like optical filtering and refractive index sensing. This paper proposes a multi narrowband perfect metamaterial absorber composed of a Si3N4 dielectric nanocavity array on a silver film. Simulation by finite element method gives four absorption bands with peak absorptances up to 99.9% and narrow bandwidth down to 0.74 nm. These absorption bands come from surface lattice resonance mode and three surface plasmon polariton modes. Besides, these modes are highly susceptible to changes in geometrical and optical parameters, which means absorption peaks can be tuned in the visible near infrared range. The refractive index sensing capability of the structure was also investigated, giving 347 nm per refractive index unit sensitivity and 469 figure of merit. These features make the proposed structure suitable for applications such as refractive index sensors and optical filters.