We develop a new strategy-proof double auction protocol characterized as average-case budget-non-negative. It is well-known that there is no strategy-proof double auction protocol that satisfies Pareto efficiency, individual rationality, and budget-balance simultaneously. The existing approach is to give up Pareto efficiency or strategy-proofness by enforcing budget-balance or budget-positive as a hard constraint. We propose a new direction to relax the budget-non-negative condition slightly. Although this protocol might take loss or profit for some cases, it it guaranteed not to exceed the predetermined amount of loss. Simulation results show that this protocol can be budget-non-negative on average and achieve social surplus that is very close to being Pareto efficient by setting parameters appropriately.