Cloud consumers need services that, in addition to meeting their business requirements, provide them with a certain level of quality of service (QoS). On the other hand, cloud providers desire to sale services corresponding to their preferences. In this situation, cloud computing service negotiation (CCSN) can be used to establish an agreement among trading parties with conflicting preferences. The CCSN allows consumer and provider negotiate together automatically on negotiable issues that are important for both trading parties. It aims to provide maximum utility for the parties in possible shortest time. In this paper, we propose a CCSN which provides simple or composite services to consumers. We introduce strategies that negotiators can choose from. We carry out some simulations to compare the performance of the strategies. Analysis of the results of simulations shows that our recommended strategy is more efficient in terms of negotiator's utility and the number of rounds spent on negotiation to reach an agreement than the others. The contributions of the proposed CCSN can be summarized as follows: (1) design and simulation of a new negotiation strategy which aims to maximize utility for both trading parties and increase the speed in reaching an agreement, (2) proposing a process for aggregating the results of negotiations on simple task requirements to ensure end-to-end composite service requirements.