The invention provides a method for leaching nickel and cobalt from low-iron and high-magnesium and high-iron and low-magnesium laterite-nickel ore by using waste dilute sulphuric acid. Nickelous hydroxide, cobaltous hydroxide and the like are directly extracted by leaching the laterite-nickel ore with non-concentrated decolored and desalinated waste dilute sulphuric acid. The method specially comprises the steps of: removing impurities out of the waste dilute sulphuric acid, slurrying, leaching and pre-neutralizing, filtering and washing leached ore pulp, settling nickel and cobalt from leachate, filtering and washing nickel and cobalt settled slurry, electrically depositing nickel, and post-treating and recycling iron, magnesium, manganese and the like. The method provided by the invention overcomes the technical difficulty, ensures that a technology of a direct dilute sulphuric acid atmospheric pressure leaching process route operates stably, is greatly lowered in cost, is high in production efficiency, and is high in recycling rate of nickel, cobalt, iron, magnesium, manganese and other metals. The waste dilute sulphuric acid which is an byproduct in industries such as dye industry and is difficult to treat is effectively recycled, the method is environmental-friendly, any harmful gas is not emitted, waste slag is solid materials, trees can be planted on the waste slag for greening, the waste slag can be recycled, and waste water can completely reach the standard for emission.