We solve a twofold ill-posed inverse problem of a nonlinear convection-diffusion equation, endowed with unknown source term and unknown moving boundary. When the solution is expanded through the superposition of a family of modified homogenization functions in a reduced domain, the unknown space-time-dependent source function can be obtained by solving a small scale linear system, with the help from the over-specified data of left flux, the measured final time data and some inner data, which are very saving. Simultaneously, the unknown moving boundary can be detected by solving nonlinear equations using the Newton iterative method. Numerical examples are given to confirm that the super-position of homogenization functions method (SHFM) can recover the unknown source function and moving boundary very well. (C) 2019 Elsevier Ltd. All rights reserved.