In this paper, we conducted a simulation of an indium-gallium-zinc oxide (IGZO)-based neuromorphic system and proposed layer-by-layer membrane capacitor (Cmem) optimization for integrate-and-fire (I&F) neuron circuits to minimize the accuracy drop in spiking neural network (SNN). The fabricated synaptic transistor exhibited linear 32 synaptic weights with a large dynamic range (~846), and an n-type-only IGZO I&F neuron circuit was proposed and verified by HSPICE simulation. The network, consisting of three fully connected layers, was evaluated with an offline learning method employing synaptic transistor and I&F circuit models for three datasets: MNIST, Fashion-MNIST, and CIFAR-10. For offline learning, accuracy drop can occur due to information loss caused by overflow or underflow in neurons, which is largely affected by Cmem. To address this problem, we introduced a layerby-layer Cmem optimization method that adjusts appropriate Cmem for each layer to minimize the information loss. As a result, high SNN accuracy was achieved for MNIST, Fashion-MNIST, and CIFAR-10 at 98.42%, 89.16%, and 48.06%, respectively. Furthermore, the optimized system showed minimal accuracy degradation under device-todevice variation.