A two-dimensional immiscible droplet deformation phenomena on moving wall in a channel has been investigated by using lattice Boltzmann method involving two-phase model. The dependence of the deformation of the droplet with different sizes on the contact angle and the velocity of bottom wall has studied. When the bottom wall starts to move, the deformation of the droplet occurs. For the largest bottom wall velocity, eventually, the deformation of the droplet is classified into the three patterns according to the contact angle.