In the real economy, many leasing problems are neither pure online leasing problems nor pure offline leasing problems, but they are online leasing problems with partially known information. In this paper, we study online problem of leasing equipment when the workload is known but the task progress is unknown. In order to minimize the cost of leasing equipment, we formulate basic mathematics model firstly, design the task track strategy TTS, and then find out that the competitive ratio of algorithm TTS is B+1B+θθ（1≤θ≤2）. Finally we compare the competitive ratio of algorithm TTS with one of the classical Karp algorithm, whose competitive ratio is 2-1B. Our results indicate that the algorithm TTS is superior to the classical online algorithm and its competitive performance is obviously improved.