The invention relates to a method for extracting nickel and cobalt from a nickel mineral, in particular to a method for extracting an intermediate product of a nickel and cobalt enrichment substance. The method is characterized in that nickel lateritic ore is processed by adopting the procedures of heap leaching, leaching, liquid neutralization, impurity removal and nickel and cobalt precipitation, and the nickel and cobalt enrichment substance is produced finally. Compared with a fire method technology and a wet method technology in the prior art, after being pulverized, the nickel lateriticore can be completely and directly processed by sulfuric acid heap leaching and also can be processed by sulfuric acid heap leaching by adjusting the proportion of heap leaching/agitation leaching according to different properties of raw materials, namely, since the permeability can not reach the requirement if the original ore is directly processed by the heap leaching,, the original ore can be graded, and part of fine particle level ore can be separated, agitated and leached, and the rest can be processed by the heap leaching. Thereby, the invention has no special requirement on the grade of the ore, has wide adaptability of the raw materials and also lowers the energy consumption and the cost. The invention adopts a method of pickling at normal pressure, has simple procedure and saves the cost. In addition, the Ni and Co recovery rate of the whole procedure of the invention is greater than 99.5% and is higher than that of a processing method in the prior art.