Parsing natural language sentences in a context-sensitive manner is a challenging task in NLP due to the ambiguity and complexity of human language. Traditional parsing techniques often fail to accurately interpret syntactic structures when the meaning of words depends on their context. In this work, we propose a context-sensitive dependency parser using a multi-layered neural network architecture that integrates BERT-based contextual embeddings and BiLSTM layers. This approach enables the model to effectively capture long-range dependencies and syntactic relationships in sentences. The parser is trained and evaluated on the Universal Dependencies English Web Treebank dataset, achieving a head prediction accuracy of 66%. Visual output demonstrates the ability of the model to handle complex sentence structures such as conditional and coordinated clauses. This research establishes a foundation for future work in fully labeled dependency parsing and highlights the effectiveness of combining contextual embeddings with deep sequence modeling for robust syntactic analysis.