Sense of access is an important yardstick for measuring the effect of precise poverty alleviation work and an important guide for rural grassroots governance work. This paper designs an evaluation index system for rural poor people’s sense of access, constructs a logistic regression model, and studies the current situation of rural poor people’s sense of access and influencing factors. Firstly, based on the idea of Modified Ridge Estimation and Liu Estimation, Modified Liu Estimation is proposed as an alternative estimation method for Great Likelihood Estimation to solve the problem of multicollinearity in binary logistic regression models. Then, 20 indicators related to the five dimensions of economy, politics, ecology, society, and culture are selected to explore and establish the evaluation system of rural poor people’s sense of access. Nineteen precision poverty alleviation administrative villages in a national poverty-stricken county in Gansu Province were selected for questionnaire distribution. It has been found that gender differences have significant effects on access to economic income. In terms of specific factors, the logistic regression equation has the greatest explanatory power for F1 economic sense of access (the value of R-squared is 0.15, p=0.000<0.001), followed by the sense of access to F4 social services (the value of R-squared is 0.12, p=0.000<0.001). In summary, this paper puts forward policy recommendations to enhance the sense of access of the rural poor, such as revitalising rural industries. This paper provides certain references for improving the grassroots social governance system and strengthening the modernization of governance capacity.