At present, privacy preserving is an important research challenge of information system security. Privacy leak detection for applications is an effective solution for privacy preserving. Taint analysis can effectively protect the confidentiality and integrity of information in the system, and report the privacy leak risk of applications in advance. However, the existing static taint analysis tool still has the problem of high analysis overhead especially in high sensitive mode. This work first deeply analyzes that there exists a large number of unrelated propagation which leads to unnecessary expenses in current IFDS-based taint analysis, and statistical results show that the proportion of it is up to 85.5%. Aiming at this problem, this paper attempts to use an effective optimization method, sparse optimization in recent years, to eliminate the unrelated propagation in static taint analysis, and achieve the optimization of time and space cost. We have innovatively extended the classic data flow analysis framework (IFDS) into a sparse form, and provide a corresponding taint analysis algorithm. We implemented a tool called FlowDroidSP. Experimental results show that the tool has 4.8 times of time acceleration and 61.5% memory reduction compared with the original FlowDroid under the non-pruning mode. Under pruning mode, it has an average time of 18.1 times speedup and 76.1% memory reduction.