Based on the characteristics of urban-rural dual economic structure in China, we build a dynamic endogenous urban-rural dual economic model closely linked to China's reality, and carry out mathematical economics analysis of optimized conditions for urban and rural sectors. The main results show that: (i) The labor growth rate of urban-rural sectors must be greater than the time discount rate, or else there would be a vicious cycle of diminishing returns in the sectors; (ii) The accumulation rate of physical capital and human capital of urban-rural sectors, and the rate of technological progress, need to be greater than the corresponding depreciation rate plus the time discount rate, otherwise there would be a vicious cycle of diminishing returns in the sectors; (iii) The low accumulation rate in the rural sector, and the occurrence of labor outflow, human capital loss and lack of investment, will expand income gap between urban and rural areas, which is a reason for solidification of urban-rural dual economic structure.