The Gaussian sum rules (GSRs) for the D(1±) and Ds(1±) mesons current are obtained by means of Laplacian transformation. Based on it, the GSRs for the mass and the coupling constants of D(1±) and Ds(1±) mesons are worked out. Using the standard input of quantum chromodynamics nonperturbative parameters, the corresponding curves and tables are presented. The results are in accordance well with the experimental data, and more well than those from the Borel sum rule approach.