We have constructed and tested a novel plastic-scintillator-based solid-state active proton target for use in nuclear spectroscopic studies with nuclear reactions induced by an ion beam in inverse kinematics. The active target system, named Stack Structure Solid organic Scintillator Active Target (S4AT), consists of five layers of plastic scintillators, each with a 1-mm thickness. To determine the reaction point in the thickness direction, we exploit the difference in the energy losses due to the beam particle and the charged reaction product(s) in the scintillator material. S4AT offers the prospect of a relatively thick target while maintaining a good energy resolution. By considering the relative energy loss between different layers, the energy loss due to unreacted beam particles can be eliminated. Such procedure, made possible by the multi-layer structure, is essential to eliminate the effect of unreacted accompanying beam particles, thus enabling its operation at a moderate beam intensity of up to a few Mcps. We evaluated the performance of S4AT by measuring the elastic proton-proton scattering using a 70-MeV proton beam at Cyclotron and Radioisotope Center (CYRIC), Tohoku University.