A method for producing nickel sulfate and cobaltous sulfate by purification of a laterite nickel ore sulfuric acid leaching solution and silica gel chelate resin, comprising: 1) grinding laterite nickel ores (limonite type, transition layer type and detritus layer type) to -0.15 mm of ore powder accounting for 95% or above; 2) adding sulfuric acid and water into the ground transition layer type laterite nickel ore to carry out atmospheric pressure leaching and separate a leaching solution 1 and filter residue 1; 3) placing the limonite type laterite nickel ore into an autoclave, and adding sulfuric acid and water to carry out high pressure leaching to separate a leaching solution 2 from a filter residue 2; 4) adding the leaching solutions into the detritus layer type laterite nickel ore to carry out neutralization, impurity removal and leaching to separate a neutralization solution and a filter residue 3; 5) adding hydrogen peroxide for reaction precipitation, and performing solid-liquid separation to separate a filtrate and a filter residue 4; 5) performing silica gel chelating resin separation on the filtrate to produce nickel sulfate and cobaltous sulfate; 6) adding pulverized coal into the filter residues, conducting magnetization roasting, then conducting weak magnetic separation to separate iron ore concentrate and tailings; 7) removing manganese from a tail liquid; and 8) discharging the tailings.