Fiber-optic distributed acoustic sensing (DAS) technology with high spatial and strain resolutions has been widely used in many practical applications. New methods to enhance the phase sensitivity of sensing fiber are worth exploring to further improve DAS performances, although the standard single-mode fiber (SSMF) has been widely used for DAS technology. In this work, we propose and demonstrate the concept of enhancing the phase sensitivity of DAS by softening the cladding of the sensing fiber, for the first time. The theoretical analysis indicates that softening sensing fiber cladding is an effective way to improve phase sensitivity. Thus, we fabricated cladding softened fibers (CSFs) and tested their phase sensitivities experimentally. According to the results, it is found that the phase sensitivity of the CSF with 0.48 WT% phosphorus-doping concentration and 80 µm cladding diameter is 22% and 54% higher than that of the non-phosphorus-doping fiber with 80 µm cladding diameter and SSMF, respectively. The results show that by reducing fiber cladding Young's modulus with higher phosphorus-doping concentration, the DAS phase sensitivity can be enhanced effectively, verifying the theoretical analysis. Also, we found that the phase sensitivity enhancement of the sensing fiber has a linear relationship with the cladding phosphorus-doping concentration, i.e. Young's modulus. In conclusion, the reported CSF paves a way for improving the DAS phase sensitivity and would be applied to other major optical fiber sensing systems as a better sensing element over SSMF due to the enhancement in the elasto-optical effect of the sensing fiber.