Adaptive spline-based methods have been applied to inverse problems in science and engineering. Those studies have shown that if proper spline bases can be chosen, problem complexity can be significantly reduced while increasing estimation accuracy and robustness against the disturbances. We proposed a mutivariate adaptive non-parametric regression spline (MARS) based approach for the solution of inverse ECG problem and assessed its robustness against measurement noise, geometric errors, and their combination. Two LV-paced experimental epicardial potential beats were obtained from University of Utah. Body surface measurements were simulated from these potentials at 30, 20 and 10 dB SNR. In the MARS approach, the unknown epicardial potential distribution was approximated by using a small number of spline functions. These spline functions were defined in terms of spatial parameters based on the given epicardial surface geometry, and selected automatically by the algorithm. Inverse problem was solved using forward matrices based on true and noisy geometric models. In the latter, geometric error was introduced as heart size error with scale 0.8 and 1.2 of original size. When only measurement noise was present; as SNR decreased from 30 to 10 dB, average correlation coefficient (CC) values decreased from 0.72 to 0.57, and 0.85 to 0.73 for Tikhonov regularization and MARS, respectively. When there was also geometric error with 0.8 size-scale; for the same SNR decrease, CC ranges became 0.7 to 0.57, and 0.78 to 0.71 for Tikhonov regularization and MARS, respectively. Finally, when there was geometric error with 1.2 size-scale; for the same SNR decrease, CC ranges were 0.7 to 0.57, and 0.80 to 0.7 for Tikhonov regularization and MARS, respectively. The proposed approach remained robust against disturbances, with average CC greater than 0.78 even if there exist measurement noise and modeling error at the same time.