  We study the geodesic equations in the space-time of neutral Brans-Dicke
Dilaton black hole in three dimensions, BTZ black holes and the 2+1 black hole.
We use the process of separation of the Hamilton-Jacobi equation to obtain the
constants of motion. The whole analytical solution of the geodesic equations in
the space-times of the intended black holes are shown completely. Moreover, the
geodesic equations are solved in terms of Weierstrass elliptic functions.
Furthermore, with use of the analytical solution and effective potential
technique some trajectories around the black holes are classified. Meanwhile,
by analytical solution, effective potential and considering the zeroes of
underlying polynomials, some possible orbits are plotted. Finally, we compare
our results with Cruz {\it et. al.} \cite{Cruz:1994ar} and we indicate the
benefits of the analytical method which is applied in this paper.
