We consider a situation where agents have to choose one project among the set of multiple alternatives and at the same time they have to agree with the way of sharing the cost of the project that is actually developed. We propose a multi-bidding cost sharing mechanism where each agent simultaneously announces his voluntary contribution for each project when the project is actually carried out, in combination with his vote for the projects. We show that a Nash equilibrium exists in this mechanism, and in any Nash equilibrium of this mechanism, the efficient project is always chosen. Moreover, in the Nash equilibrium, the way of sharing the cost of the project is, in a sense, an equal sharing rule.