This paper presents the improved vibration attenuation performance obtained from a new type of acoustic metamaterial, built by attaching cantilever-type resonators (CR) and lever-type inertial amplification mechanisms (LIA) to a host beam. The LIA mechanism consists of one horizontal bar and two vertical bars and connected by hinges. The band structure of a unit cell and the vibration transmissibility of finite structure are calculated by finite element method. Numerical results show that the wave attenuation ability of the present structure is enhanced and better than the LR beam with the same additional mass. To reveal the physiccal mechanism of CR-LIA beam under different structural parameters, effect of mass ratio and amplification ratio are investigated. It is found that for both of the two ways, it shows a similar effect of moving starting bandgap to lower frequency with increase of them. While for some specific situation, extending the length of the lever of LIA mechanism is a feasible way comparing with adding the mass.