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Although second‐order cone programming (SOCP) has been applied to optimise camera parameters in computer vision, it is occasionally been used to refine fisheye camera external parameters as well. This study presents a fisheye camera external parameter estimation based on SOCP in convex optimisation. The homography constraint between two spherical images are first exploited to derive an equation with respect to a given error threshold. Then, the fisheye camera external estimation is transformed into an SOCP optimisation problem through reformulating the parameter estimation equation. The SOCP method has been implemented in Matlab and the optimisation toolbox has been made publicly available. The fisheye camera external parameter optimisation method has been validated by some experiments with synthetic and real data. Comparison experiments between the proposed method and other methods in the literature are also carried out, and the results show that the SOCP method is better for the corrected images.