The Lattice Boltzmann Equation (LBE) method has recently emerged as a powerful tool of computational fluid dynamics, especially for simulation of complex and multi phase fluids, as opposed to conventional methods based on solution of Navier–Stokes equations. Simulations of multi component and multi phase flows are the most important problems in the fluid mechanical engineering, according to the wide variety of practical applications in industrial processes. So a lot of lattice Boltzmann models has been assigned to multiphase problems. Shan and Chen proposed a LB multiphase model which utilizes a non-local interaction force between particles at neighboring lattice sites, thereby generating spurious currents at the interface and also the local momentum conservation was not satisfied. However, single component multiphase flows can be simulated by this model and it is possible to expand it to handle problems with an arbitrary number of components with different molecular masses. In these cases the interaction potentials are defined for each of the components, which control the form of the equation of state of the fluid. In this dissertation, the multi component multi phase Lattice Boltzmann Model (LBM) introduced by Shan and Chen is applied numerically to study its abilities to simulate the physics of multiphase flows. The benchmark test is the simulation of a static droplet immersed in a periodic domain of another fluid. The results showed that Shan-Chen model is not able to simulate multi component systems with density ratio greater than one between two fluids. The above mentioned drawback caused by the nonphysical definition of the inter particle interaction force in this model. The Shan-Chen model only used a single repulsive force between the particles of the two components in the interface. The objective of this thesis is to improve the Shan-Chen model to simulate multi component flows with higher density ratio between two fluids. In the new model, an inter particle interaction force is added to each phase particles. The results show that the new model is able to simulate multi component flows with density ratio greater than two. The surface tension in the Shan-Chen model is a parameter which is determined by the Laplace law also it cannot be changed and adjusted in a favorite manner. But in the new model, surface tension could be adjusted by changing interaction forces.In addition to the above results, simulations of droplet on hydrophilic and hydrophobic surface are performed and the fluid-solid contact angle is examined. The results showed that, the shan-Chen multi component model has the ability of simulating static contact angle of the droplet from hydrophobic to hydrophilic.