Hand gesture-based Sign Language Recognition (SLR) serves as a crucial communication bridge between deaf and non-deaf individuals. Existing SLR systems perform well for their cultural SL but may struggle with multi-cultural sign languages (McSL). To address these challenges, this paper proposes a Stack Spatial-Temporal Transformer Network that leverages multi-head attention mechanisms to capture both spatial and temporal dependencies with hierarchical features using the Stack Transfer concept. In the proceed, firstly, we applied a fully connected layer to make a embedding vector which has high expressive power from the original dataset, then fed them a stack newly proposed transformer to achieve hierarchical features with short-range and long-range dependency. The network architecture is composed of several stages that process spatial and temporal relationships sequentially, ensuring effective feature extraction. After making the fully connected layer, the embedding vector is processed by the Spatial Multi-Head Attention Transformer, which captures spatial dependencies between joints. In the next stage, the Temporal Multi-Head Attention Transformer captures long-range temporal dependencies, and again, the features are concatenated with the output using another skip connection. The processed features are then passed to the Feed-Forward Network (FFN), which refines the feature representations further. After the FFN, additional skip connections are applied to combine the output with earlier layers, followed by a final normalization layer to produce the final output feature tensor. This process is repeated for 10 transformer blocks. The extensive experiment shows that the JSL, KSL and ASL datasets achieved good performance accuracy. Our approach demonstrates improved performance in McSL, and it will be consider as a novel work in this domain.