Apache Storm, a typical platform for big data stream computing, uses a round-robin scheduling algorithm as the default scheduler, which does not consider the fact that differences of computational and communication cost are ubiquitous among different tasks and different data streams in one topology. Hence optimization is needed in terms of load balance and communication cost. To solve this problem, a Task Scheduling Algorithm based on Weight in Storm (TSAW-Storm) was proposed. In the algorithm, CPU occupation was taken as the weight of a task in a specific topology, and similarly tuple rate between a pair of tasks was taken as the weight of a data stream. Then tasks were assigned to the most suitable work node gradually by maximizing the gain of weight of data streams via transforming inter-node data streams into intra-node ones as many as possible with load balance ensured in order to reduce network overhead. Experimental results show that TSAW-Storm can reduce latency and inter-node tuple rate by about 30.0% and 32.9% respectively, and standard deviation of CPU load of work nodes is only 25.8% when compared to Storm default scheduling algorithm in WordCount benchmark with 8 work nodes. Additionally, online scheduler is deployed in contrast experiment. Experimental results show that TSAW-Storm can reduce latency, inter-node tuple rate and standard deviation of CPU load by about 7.76%, 11.8% and 5.93% respectively, which needs only a bit of executive overhead compared to online scheduler. Therefore, the proposed algorithm can reduce communication cost as well as improve load balance effectively, which makes a great contribution to the efficient operation of Apache Storm.