We report a novel framework for achieving fragment-based molecular design using pixel convolutional neural network (PixelCNN) combined with the simplified molecular input line entry system (SMILES) as molecular representation. While a widely used recurrent neural network (RNN) assumes monotonically decaying correlations in strings, PixelCNN captures a periodicity among characters of SMILES. Thus, PixelCNN provides us with a novel solution for the analysis of chemical space by extracting the periodicity of molecular structures that will be buried in SMILES. Moreover, this characteristic enables us to generate molecules by combining several simple building blocks, such as a benzene ring and side-chain structures, which contributes to the effective exploration of chemical space by step-by-step searching for molecules from a target fragment. In conclusion, PixelCNN could be a powerful approach focusing on the periodicity of molecules to explore chemical space for the fragment-based molecular design.