The layered crystal of EuSn_{2}As_{2} has a Bi_{2}Te_{3}-type structure in rhombohedral (R3[over ¯]m) symmetry and has been confirmed to be an intrinsic magnetic topological insulator at ambient conditions. Combining ab initio calculations and in situ x-ray diffraction measurements, we identify a new monoclinic EuSn_{2}As_{2} structure in C2/m symmetry above ∼14 GPa. It has a three-dimensional network made up of honeycomblike Sn sheets and zigzag As chains, transformed from the layered EuSn_{2}As_{2} via a two-stage reconstruction mechanism with the connecting of Sn-Sn and As-As atoms successively between the buckled SnAs layers. Its dynamic structural stability has been verified by phonon mode analysis. Electrical resistance measurements reveal an insulator-metal-superconductor transition at low temperature around 5 and 15 GPa, respectively, according to the structural conversion, and the superconductivity with a T_{C} value of ∼4 K is observed up to 30.8 GPa. These results establish a high-pressure EuSn_{2}As_{2} phase with intriguing structural and electronic properties and expand our understandings about the layered magnetic topological insulators.