This paper presents a study of the motion of a deformable droplet modeled using Shan-Chen (SC) Multiphase Lattice Boltzmann Model (LBM). Firstly, a 2D static droplet in a periodic domain is modeled such that its surface tension is numerically determined and successfully validated against Young-Laplace equation. Next, simulation of a 2D droplet transported by a gas stream along a periodic microchannel is carried out. Initially, the droplet is placed close to the top wall and surrounded by a gas stream which is originally flowing in fully developed condition, as described by the classical plane Poiseuille flow. Both the droplet and the carrier fluid have same kinematic viscosities but different densities. The simulation is extended until pseudo-steady state, determined by a constant vertical position and normalized velocity, is reached. The results of this study are successfully validated using available data from previous highly-accurate numerical work. The LBM demonstrated a number of major advantages such as easiness to set up, ability to track the phase interface automatically and its inherent parallel capacity which helped reducing the computational time. However, numerical results obtained with the SC-LBM, which is presented in this study, demonstrate that the LBM also has limitations in handling large density and viscosity ratios between the phases.