This paper proposes a collaborative color calibration method for multi-camera systems. The multi-camera color calibration problem is formulated as an overdetermined linear system, in which a dynamic range shaping is incorporated to ensure the high contrasts for captured images. The cameras are calibrated with the parameters obtained by solving the linear system. For non-planar multi-camera systems, we design a novel omnidirectional color checker and present a method for establishing global correspondences to facilitate automatic color calibration without manual adjustment. According to experimental results on both synthetic and real-system datasets, the proposed method shows high performance in achieving inter-camera color consistency and high dynamic range. Thanks to the generality of the linear system formulation and the flexibility of the designed color checker, the proposed method is applicable to various multi-camera systems.