Free energy based lattice Boltzmann method (LBM) has been used to simulate the contact angle and the bubble necking with large density ratio. LBM with the proper contact angle model is able to reduce the spurious currents and eliminate the singularity in the contact lines. The numerical results of the contact angles are satisfied with the Youngs law. For bubble necking flows, simulations are executed for various viscosities and contact angles. The phenomena of the bubble necking are simulated successfully and the subsequent results are presented. The present method is also applicable to the nucleate boiling flows.