For GI/G/1 queue, we transfer the problem of the law of iterated logarithm for queue length process, busytime process and the workload process into problems related to reflected Brownian Motion. By using properties of reflected Brownian Motion, we get the functional law of iterated logarithm forqueue length process, busy time process and the workload process and determine the parameters. The method based on strong approximation can be applied for multi-class queue network.