Currently, compared to the situation of aging population and the demand for elderly care services from the people, the overall quality and level of development of elderly care services in China are not high. The community home-based elderly care services quality evaluation for disabled elderly people could be looked as the multiple-attribute decision-making (MADM). The TOPSIS technique is a useful technique to put up with the MADM. The probabilistic simplified Neutrosophic set (PSNSs) is easy to express uncertain information during community home-based elderly care services quality evaluation for disabled elderly people. In this study, CRITIC technique is put forward to obtain the attribute weights and the probabilistic simplified neutrosophic number TOPSIS (PSNN-TOPSIS) technique is put forward for MADM. Finally, numerical example for community home-based elderly care services quality evaluation for disabled elderly people is employed to verify the PSNN-TOPSIS technique with comparative analysis.