In one-dimensional trapped Bose-Fermi mixture, described by time-dependent one-dimensional nonlinear equations that are derived from a three-dimensional Bose-Fermi system, we study the effect of atom-interactions on stability using a Gaussian Variational approach. We investigate the stable and the unstable conditions as functions of the atoms number and s-wave scattering length. We find that the interaction between the different species of atoms has significant effect on the stability of Bose-Fermi mixture. We also give critical conditions of the atoms number and s-wave scattering length for both special and general cases.