The invention provides a modified asphalt composition with a creeping characteristic, which comprises the following components in parts by weight: 15-60 parts of asphalt, 3-15 parts of modifying material, 5-30 parts of rubber powder, 15-60 parts of softening agent, 15-60 parts of inorganic powder, 3-25 parts of viscosity regulating agent, 0.3-1.5 parts of peptizing agent and 0.1-2 parts of coupling agent. A preparation method of the modified asphalt composition comprises the following steps of: adding the softening agent into a reaction kettle, heating to 170 to 200 DEG C, adding the modifying material, agitating, adding the asphalt and the rubber powder, and agitating for 1-2 h to obtain an intermediate raw material; levigating the intermediate raw material to 150-250 meshes, and putting back to the reaction kettle; and finally, adding the inorganic powder, the viscosity regulating agent, the peptizing agent and the coupling agent into the reaction kettle, agitating and dispersing uniformly. The modified asphalt composition has the characteristics of excellent water-proof performance, strong binding capability and continuous binding capability, large elongation percentage and good low-temperature flexibility.