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To prolong the lifetime of Wireless Sensor Networks, we investigate a minimax fair scheduling in the multi-access transmission. We search for the minimax optimal power tuple in the dominant face of the multi-access power contra-polymatroid, where the sum power of the sensor nodes is minimized. Because a time sharing of the vertices can achieve any base, the searching problem is then converted to a linear optimization problem computing the time sharing coefficients. This computation problem is then divided into independent parts and solved in parallel by the sensor nodes. Simulation results show that the proposed strategy substantially prolongs the lifetime of sensor networks, compared with the TDMA transmission and energy minimized transmission. Moreover, the proposed strategy directly output the system parameters to achieve the minimax scheduling and is favorable to compute and apply in practice.