The memristive neuromorphic computing system (MNCS) can complete related calculations with lower power consumption and higher speed, which has attracted widespread attention. However, due to the limitations of memristor and circuit, the realization of MNCS faces many challenges. In this paper, we propose a heterogeneous deployment strategy for the MNCS and construct a lightweight heterogeneous memristive gas classification neural network (LHM-GSNN) based on the electronic nose (e-nose) application. In addition, the model parameters are quantified by clustering strategy to adapt to the nonideal characteristics of memristor. The experimental results show that the complex structure in the model is visibly simplified, and the number of parameters is correspondingly reduced using the heterogeneous deployment strategy. Furthermore, we also analyze the power consumption of the LHM-GSNN model deployed to the MNCS. This work may provide new solutions for constructing and implementing the MNCS.