This paper presents an FPGA-based streaming computation for the lattice Boltzmann method (LBM) to simulate fluid flow with floating-point calculations. LBM is suitable for streaming computation because of its parallelism and regularity. We optimize the equations of LBM, and then formulate a streaming computation. To design an efficient data-path for throughput and hardware resource utilization, we introduce multiple cycle inputs and computing-unit sharing to the streaming data-path. The streaming accelerator implemented on a Virtex-4 FPGA with PCI-Express x8 interface achieves 2.93 and 2.46 times faster computation than a 3.4GHz Pentium4 processor and a 2.2GHz Opteron processor, respectively, for 2-dimensional time-dependent fluid dynamics problems.