For many capacitive power transfer (CPT) systems, load-independent constant current (CC) output characteristics can improve load adaptation of topologies and is main process of charging. Load-independent zero phase angle characteristic can decrease reactive power mostly and improve efficiency. High voltages on four coupling plates are very easy to cause air breakdown and also deteriorate the electromagnetic interference (EMI) issue, which limits the transfer power. In this work, different resonance conditions of CC output with ZPA for LCLC-LC compensated CPT systems are analyzed and the case with minimum parameter constraints is designed. In the proposed system, accurate load-independent ZPA characteristic and minimum voltage stresses on coupler plates can be designed in theory. Besides, the design method of CC output with ZPA and voltage stress optimization is based on gyrator method and can simplify the complexity of analysis.