Multivariate time series alignment is critical for ensuring coherent analysis across variables, but missing values and timestamp inconsistencies make this task highly challenging. Existing approaches often rely on prior imputation, which can introduce errors and lead to suboptimal alignments. To address these limitations, we propose a constraint-based alignment framework for incomplete multivariate time series that avoids imputation and ensures temporal and structural consistency. We further design efficient approximation algorithms to balance accuracy and scalability. Experiments on multiple real-world datasets demonstrate that our approach achieves superior alignment quality compared to existing methods under varying missing rates. Our contributions include: (1) formally defining incomplete multiple temporal data alignment problem; (2) proposing three approximation algorithms balancing accuracy and efficiency; and (3) validating our approach on diverse real-world datasets, where it consistently outperforms existing methods in alignment accuracy and the number of aligned tuples.