Large-scale streaming matrix multiplication is very common in various applications, sparking significant interest in develop efficient algorithms for approximate matrix multiplication (AMM) over streams. In addition, many practical scenarios require to process time-sensitive data and aim to compute matrix multiplication for most recent columns of the data matrices rather than the entire matrices, which motivated us to study efficient AMM algorithms over sliding windows. In this paper, we present two novel deterministic algorithms for this problem and provide corresponding error guarantees. We further reduce the space and time costs of our methods for sparse matrices by performing an approximate singular value decomposition which can utilize the sparsity of matrices. Extensive experimental results on both synthetic and real-world datasets validate our theoretical analysis and highlight the efficiency of our methods.