Based on the Gross-Pitaevskii (G-P) energy functional, the Anderson localization of a weakly-interacting Bose-condensed gas in a controllable speckle potential was investigated by means of split-step Fourier spectral method. The conclusions are as following. 1) The Gaussian-like exponential ansatz achieves good results in variation analysis. 2) Under the condition that disorder strength η is 1, interaction between atoms κ is 0.1 and characteristic intensity of speckle potential Vs is greater than 0.6 times of chemical potential μ, Bose-condensed gas can maintain a stable localized state during evolution. 3) The larger interaction between atoms goes against the formation of a stable Anderson localization when κ is greater than 5. 4) Under the condition that Vs is 0.6 μ and κ is 0.1, Anderson localization of Bose-condensed gas is more notable as the disorder strength of speckle potential η increases.