The invention discloses a method for selective extraction of nickel, cobalt and iron from laterite-nickel ore. The method comprises the following steps: laterite nickel ore is crushed, sodium fluoride and water are added with fully mixing, and a mixture is obtained; concentrated sulfuric acid is sprayed into the mixture, activation treatment is carried out in a self-heating state, in order to prepare an activated material; normal pressure water immersion is carried out for the activated material in order to obtain leached pulp; thickening separation is carried out for the leached pulp in order to obtain leachate and leached residue; washing is carried out for the leached residue in order to obtain iron slag; magnesium oxide is used for neutralizing the leachate and precipitating nickel-cobalt in order to obtain separating liquid after neutralization and hydroxide of nickel-cobalt; precipitation, defluorination, evaporative crystallization are carried out in order for separating liquid after neutralization in order to recover magnesium sulfate. The method can be applied to realization of high efficient selective leaching of nickel and cobalt in a mild condition without external heating and pressurization, leaching rate reaches 90% or above, leaching rate of iron reaches 1% or below, so that high efficient selective separation of nickel, cobalt and iron in laterite-nickel ore is better realized.