In data-parallel computing frameworks, intermediate parallel data is often produced at various stages which needs to be transferred among servers in the datacenter network (e.g. the shuffle phase in MapReduce). A stage often cannot start or be completed unless all the required data pieces from the preceding stage are received. \emph{Coflow} is a recently proposed networking abstraction to capture such communication patterns. We consider the problem of efficiently scheduling coflows with release dates in a shared datacenter network so as to minimize the total weighted completion time of coflows. Several heuristics have been proposed recently to address this problem, as well as a few polynomial-time approximation algorithms with provable performance guarantees. Our main result in this paper is a polynomial-time deterministic algorithm that improves the prior known results. Specifically, we propose a deterministic algorithm with approximation ratio of $5$, which improves the prior best known ratio of $12$. For the special case when all coflows are released at time zero, our deterministic algorithm obtains approximation ratio of $4$ which improves the prior best known ratio of $8$. The key ingredient of our approach is an improved linear program formulation for sorting the coflows followed by a simple list scheduling policy. Extensive simulation results, using both synthetic and real traffic traces, are presented that verify the performance of our algorithm and show improvement over the prior approaches.