The aging of lines has a strong impact on the economy and safety of the distribution network. This paper proposes a novel approach to conduct line aging assessment in the distribution network based on topology verification and parameter estimation. In topology verification, the set of alternative topologies is firstly generated based on the switching lines. The best-matched topology is determined by comparing the difference between the actual measurement data and calculated voltage magnitude curves among the alternative topologies. Then, a novel parameter estimation approach is proposed to estimate the actual line parameters based on the measured active power, reactive power, and voltage magnitude data. It includes two stages, i.e., the fixed-step aging parameter (FSAP) iteration, and specialized Newton-Raphson (SNR) iteration. The theoretical line parameters of the best-matched topology are taken as a warm start of FSAP, and the fitted result of FSAP is further renewed by the SNR. Based on the deviation between the renewed and theoretical line parameters, the aging severity risk level of each line is finally quantified through the risk assessment technology. Numerous experiments on the modified IEEE 33-bus and 123-bus systems demonstrate that the proposed approach can effectively conduct line aging assessment in the distribution network.