Coupling errors are major threats to the accuracy of 3-axis force sensors. Design of decoupling algorithms is a challenging topic due to the uncertainty of coupling errors. The conventional nonlinear decoupling algorithms by a standard Neural Network (NN) are sometimes unstable due to overfitting. In order to avoid overfitting and minimize the negative effect of random noises and gross errors in calibration data, we propose a novel nonlinear static decoupling algorithm based on the establishment of a coupling error model. Instead of regarding the whole system as a black box in conventional algorithm, the coupling error model is designed by the principle of coupling errors, in which the nonlinear relationships between forces and coupling errors in each dimension are calculated separately. Six separate Support Vector Regressions (SVRs) are employed for their ability to perform adaptive, nonlinear data fitting. The decoupling performance of the proposed algorithm is compared with the conventional method by utilizing obtained data from the static calibration experiment of a 3-axis force sensor. Experimental results show that the proposed decoupling algorithm gives more robust performance with high efficiency and decoupling accuracy, and can thus be potentially applied to the decoupling application of 3-axis force sensors.