A simulation model of electrical percolation through a three-dimensional network of curved CNTs is developed in order to analyze the electromechanical properties of a highly stretchable fiber strain sensor made of a CNT/polymer composite. Rigid-body movement of the curved CNTs within the polymer matrix is described analytically. Random arrangements of CNTs within the composite are generated by a Monte-Carlo simulation method and a union-find algorithm is utilized to investigate the network percolation. Consequently, the strain-induced resistance change curves are obtained in a wide strain range of the composite. In order to compare our model with experimental results, two CNT/polymer composite fibers were fabricated and tested as strain sensors. Their effective CNT volume fractions are estimated by comparing the experimental data with our simulation model. The results confirm that the proposed simulation model reproduces well the experimental data and is useful for predicting and optimizing the electromechanical characteristics of highly stretchable fiber strain sensors based on CNT/polymer composites.