With the soaring personal and enterprise computation demands, the scale of cloud centers has been rapidly increasing, which leads to massive amounts of greenhouse gas emission. From the cloud service provider’s (CSP) perspective, profit is the key factor to maintain the development of cloud centers, which potentially conflicts with the goal of achieving green data centers for environment protection because the expensive renewable energy will add more cost. This paper addresses the problem of maximizing profit while meeting the green degree constraints for a large scale data center on renewable energy source. Taking into account of the bursty randomness of workload, time-varying electricity price and intermittent green energy, we first formulate the problem in an optimization framework with stochastic constraints for delay-tolerant workload. Then, we show how the deployment of Lyapunov optimization technique can leverage to obtain a low-complexity online solution for profit maximization by combining request admission control, workload scheduling and power management. Moreover, we adopt a non-linear submodular revenue function to optimize the throughput of the system. By decoupling the optimization function of a time average problem into three sub-problems, we solve them to obtain the optimal control strategies. Our proposed algorithm achieves a desirable profit-green tradeoff. At the end, we provide the performance bound of our algorithm, and evaluate its performance through extensive trace-driven simulations.