In this paper, a pendulum type metamaterial (PTM) is designed with a pendulum bob hinged at the primary mass. The nonlinear dynamic model of PTM unit cell is presented with the aid of the Bloch theorem. The analytical formula of dispersion equation is deduced from the nonlinear model using the harmonic balance method. The obtained bandgap of the innovative metamaterial is in good agreement with the numerical result, thus validating the presented model. The nonlinear frequency band structure of PTM is investigated and compared with that obtained from linearized PTM model. It is found that the local resonant bandgap is tunable, and the nonlinear geometric influence of pendulum on PTM bandwidth is significant. The effects of 1:1, 1:1/2 and 1:1/3 internal resonance on the dispersion characteristics are analyzed with large swinging angle. The upper boundaries of the frequency bandgap under 1:1/2 and 1:1/3 internal resonance rise nonlinearly with the characteristic frequency of the secondary system to higher than those under linear and 1:1 internal resonance conditions. The mass coefficient gradually increases the width of PTM bandgap and PTM can possess a broader bandgap with optimized parameters.