Second magnetization peak (SMP) in hole-doped cuprates and iron pnictide superconductors has been widely explored. However, similar feature in the family of electron-doped cuprates is not common. Here, we report the vortex dynamics study in the single crystal of an electron-doped cuprate Pr$_{0.87}$LaCe$_{0.13}$CuO$_4$ superconductor using dc magnetization measurements. A SMP feature in the isothermal $M(H)$ was observed for $H$$parallel$$ab$-planes. On the other hand, no such feature was observed for $H$$parallel$$c$-axis in the crystal. Using magnetic relaxation data, a detailed analysis of activation pinning energy via collective creep theory suggests an elastic to plastic creep crossover across the SMP. Moreover, for $H$$parallel$$ab$, a peak in the temperature dependence of critical current density is also observed near 7 K, which is likely be related to a dimensional crossover (3D-2D) associated to the emergence of Josephson vortices at low temperatures. The anisotropy parameter obtained $gamma$ $approx$ 8-11 indicates the 3D nature of vortex lattice mainly for $H$$parallel$$c$-axis. The $H$-$T$ phase diagrams for $H$$parallel$$c$ and $H$$parallel$$ab$ are presented.
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