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As the Internet of Things evolves, connected vehicles create a positive impact on future traffic management systems, particularly at intersections. This study proposes a distributed, cooperative negotiation method for connected vehicles at a signal-free intersection, in which the connected vehicles exchange information with each other and perform cooperative negotiation-based control to pass the intersection without excessive stops. The vehicles optimize their desired travel times through a bilateral negotiation mechanism with safety rule constraints. Via the simulations conducted in the Simulation of Urban Mobility simulator, it shows that the proposed strategy outperforms a fixed-time signalized control, an adaptive signalized control, and a first-come-first-serve policy-based signal-free control method regarding average travel time and average travel speed.