In this paper, we propose a high-precision memristive neural network with neurons implemented by complementary metal oxide semiconductor (CMOS) inverters. Regarding the process variations in the memristors and the sensitivity of the memristive crossbar structure to these fluctuations, the read operation with repetitive pulses and feedback-based write in the memristors are used to implement the neural networks trained by the ex-situ method. Moreover, accurate modeling of the neuron circuit (CMOS inverter) and decreasing the mismatch between trained weights and the limited memristances fill the gap between simulation and implementation. To employ physical constraints based on the memristor framework during the training phase, a linear function is utilized to map the trained weights to the acceptable range of memristances after the training phase. To solve the vanishing gradient problem due to the use of the tanh function as an activation function and for better learning of the network, some measures are taken. Moreover, fin field-effect transistor (FinFET) technology is used to prevent the reduction of the accuracy of the inverter-based memristive neural networks due to the process variations. Overall, our implementation improves the speed, area, power-delay product (PDP), and mean square error (MSE) of the training stage by 91.43%, 95.06%, 48.29% and 81.64%, respectively.