A: The Cooling Storage Ring (CSR) External-target Experiment(CEE) is the first multipurpose nuclear physics experimental device to operate in the GeV energy range at the Heavy-Ion Research Facility(HIRFL-CSR) in Lanzhou, China. The primary goals of the CEE are to study the bulk properties of dense matter and to understand the quantum chromo-dynamic (QCD) phase diagram by measuring the charged particles produced in heavy-ion collisions at the target region with large acceptance. An inner time of flight (iTOF) system has been proposed to measure the multiplicity, angular distribution, and time information of the charged particles. Herein, we introduce the performance requirements of iTOF according to calculations and GEANT4 simulations. The proposed system is characterized by high granularity and time performance, hence, the conceptual design of the iTOF wall adopts high granularity Multi-gap Resistive Plate Chambers (MRPC) with a time resolution around 30 ps. To evaluate the MRPC design, the cosmic ray test was performed. A timing resolution better than 28 ps and an efficiency better than 98% have been achieved for MIPs, as interpreted by the cosmic ray GEANT4 simulation of time jitter components.