Materials development requires numerous numbers of trial and error experiments. To reduce the experimental cost, numerical simulations which predict material microstructures and mechanical properties have a great potential to estimate the microstructures that should be produced for obtaining materials with the desired properties. There is a need to develop dual-phase (DP) steel with higher strength and ductility because DP steel is widely used due to its significant mechanical properties. DP steel consists of a soft phase (ferrite) and a hard phase (martensite), and the mechanical properties depend on the ratio of the two phases. The mechanical properties of DP steels are affected by the spatial distribution of martensite and ferrite, which requires a comprehensive consideration of a variety of microstructures. The problem is how to estimate microstructures of DP steel with the desired mechanical property because a comprehensive investigation of microstructures makes computational cost significantly expensive. For the purpose of reduction of the computational costs, we aim to develop a framework with low computational cost. The developed framework finds the optimal microstructure of DP steel by repeated random searches for a model that combines a generative adversarial network (GAN), which generates microstructures, and a convolutional neural network (CNN), which predicts the maximum stress and working limit strain from microstructures. Due to a low-dimensional search space provided by a latent variable of GAN, the proposed framework enables an efficient search for microstructures possible. To explore the desired microstructures under complex deformation modes, the multiple deformation modes are considered in this study. This framework is applicable not only for the microstructure of DP steel but also any other material microstructures. We are exhaustively able to explore the microstructure with desired properties of metallic or other composite materials in low-dimensional space thanks to this framework and contributes to accelerating materials development.