Binary code similarity detection (BCSD) is a method for identifying similarities between two or more slices of binary code (machine code or assembly code) without access to their original source code. BCSD is often used in many areas, such as vulnerability detection, plagiarism detection, malware analysis, copyright infringement and software patching. Numerous approaches have been developed in these areas via graph matching and deep learning algorithms. Existing solutions have low detection accuracy and lack cross-architecture analysis. This work introduces a cross-platform graph deep learning-based approach, i.e., GraphConvDeep, which uses graph convolution networks to compute the embedding. The proposed GraphConvDeep approach relies on the control flow graph (CFG) of individual binary functions. By evaluating the distance between two embeddings of functions, the similarity is detected. The experimental results show that GraphConvDeep is better than other cutting-edge methods at accurately detecting similarities, achieving an average accuracy of 95% across different platforms. The analysis shows that the proposed approach achieves better performance with an area under the curve (AUC) value of 96%, particularly in identifying real-world vulnerabilities.