We use angle-resolved photoemission spectroscopy (ARPES) to study the electronic properties of CaFe2As2-parent compound of a pnictide superconductor. We find that the structural and magnetic transition is accompanied by a three- to two-dimensional (3D-2D) crossover in the electronic structure. Above the transition temperature (T_{s}) Fermi surfaces around Gamma and X points are cylindrical and quasi 2D. Below T_{s}, the Gamma pocket forms a 3D ellipsoid, while the X pocket remains quasi 2D. This finding strongly suggests that low dimensionality plays an important role in understanding the superconducting mechanism in pnictides.