How to efficiently dissipate the heat of a large-area hot source is an urgent problem to be solved in the thermal management field of electronic devices. Herein, multi-stage planar thermoelectric coolers (TECs) oriented to the efficient planar heat dissipation for large-area hot source are designed, and a comprehensive numerical analysis focusing on the cooling performance of the coolers for a heat source is performed by the finite-element methods. The effect of input current, thickness of thermoelectric legs, stage numbers in heat transfer area, numbers of p-n pair in each stage, heat resistance between each stage, and contact status between heat sources and coolers are studied. The results show that high cooling performance of the coolers relies on an optimized input current, large thickness of thermoelectric legs, optimized stage number and number of p-n pair, and low heat resistance between each stage and between heat sources and coolers. The optimized multi-stage planar TEC can realize a maximum cooling temperature difference of 8.2 K. This work indicates that the multi-stage planar TECs can have potential application in thermal management of electronic devices.