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This paper proposes a distance weighted biased averaging procedure (DWBAP) and applies it to the high-order finite volume method on unstructured grids. Unlike the initial BAP limiter, we use the inverse distance weighting for biased function of gradients of flow variables, and meanwhile introduce the standard deviation coefficient of the reconstruction stencil to determine the value of the distance weighting. This can efficiently maintain both the property of high precision in smooth regions and control numerical oscillations in discontinuities. Through various numerical examples, it is demonstrated that the developed DWBAP limiter can capture strong shock waves and have a good property of convergence.