The use of conductive polymer composites as strain sensors has been widely investigated due to their excellent elasticity and sensitivity. Such sensors may be manufactured using additive manufacturing techniques but there are some challenges to overcome in terms of performance if this technique is to be used. In this work, highly elastic strain sensors of carbon nanotube/thermoplastic polyurethane (CNT/TPU) nanocomposites were fabricated using fused deposition modeling (FDM), and 1-pyrenecarboxylic acid (PCA) was introduced to non-covalently modify the CNTs and improve the polymer-nanofiller interactions. The results show that the electrical and sensing properties of the modified nanocomposites are significantly increased as a result of more uniform CNT dispersion. The 3D printed sensors demonstrate outstanding performance with high sensitivity, large workable strain, excellent repeatability and regular signal responses within a wide measuring frequency range of 0.01~1 Hz. Also, the strain sensing ability of the sensor is greatly improved with the introduction of PCA.