The invention discloses a Fe-based amorphous or nanocrystalline soft magnetic alloy, aiming to favorable performance and low cost. Alloy components can be expressed as FeaSibBcCudNbeMf, wherein M is Al, Ni or P; a, b, c, d, e and f are atom percentages, and the change range is as follows: a is more than or equal to 65 and less than or equal to 85, b is more than or equal to 5 and less than or equal to 20, c is more than or equal to 5 and less than or equal to 25, d is more than or equal to 0 and less than or equal to 5, e is more than or equal to 0 and less than or equal to 5, and f is more than or equal to 0.1 and less than or equal to 10; and a+b+c+d+e+f=100. The preparation method comprises the following steps: placing raw materials of pure ferrum, pure copper, and the like into a vacuum electric arc furnace to smelt to obtain an alloy ingot; crushing, placing into a quartz test tube, and preparing an amorphous alloy ribbon by using a single-rolling ribbon throwing method; placing into a tubular annealing furnace, adjusting the temperature to 510-580 DEG C, isothermally annealing under the protection of Ar gas and getting out of the furnace to cool; and obtaining amorphous alloys with different microstructures or nanocrystalline alloys with nanometer crystal particles evenly arranged on an amorphous matrix through controlling alloy cooling speed and heat treatment temperature as well as time.