This study is purposed to derive the equation of motion for geodesics in vicinity of spacetime of a (2 + 1)-dimensional charged BTZ black hole. In this paper, we solve geodesics for both massive and massless particles in terms of Weierstrass elliptic and Kleinian sigma hyper-elliptic functions.Then we determine different trajectories of motion for particles in terms of conserved energy and angular momentum and also using effective potential. * Electronic address: rsk@guilan.ac.ir 1