Inverter-based memristive neural networks have the advantages of much lower power consumptions and higher speeds compared to those of digital implementations while they suffer from accuracy degradation due to the circuit elements variations. In this brief, we propose a circuit-level method, called RIM (Resistor-Inverter based Memristive neural network) to mitigate the accuracy degradation of this type of neural network implementation at the presence of variations as well as improve the efficacy of its offline training. In the proposed method, the high slope of the inverter voltage transfer characteristic (VTC) is reduced by adding a grounded resistor to the inverter output node. While decreasing the resistance, generally, suppresses the adverse effects of variations on the network accuracy as well as the loading effect of the memristive crossbar, it may lead to output accuracy decrease under the nominal (no variation) condition. Thus, some trade-off is considered for choosing a proper value for the added resistance. The study reveals that RIM can improve the output accuracy in the range of 10%-96% (51%-74%) in the nominal condition (variations condition).