Cubic NaYF4:Yb3+(20%)/Er3+(1%) microspheres were synthesized by EDTA-assisted hydrothermal method. Under 980 nm excitation, ultraviolet ((4)G(11/2)-->I-4(15/2)), violet (H-2(9/2)-->I-4(15/2)), green (F-4(7/2)-->I-4(15/2), H-2(11/2)-->I-4(15/2), and S-4(3/2)-->I-4(15/2)), and red (F-4(9/2)-->I-4(15/2)) upconversion fluorescence were observed. The number of laser photons absorbed in one upconversion excitation process, n, was determined to be 3.89, 1.61, 2.55, and 1.09 for the ultraviolet, violet, green, and red emissions, respectively. Obviously, n=3.89 indicated that a four-photon process was involved in populating the (4)G(11/2) state, and n=2.55 indicated that a three-photon process was involved in populating the F-4(712)/H-2(11/2)/S-4(3/2) levels. For the violet and red emissions, the population of the states H-2(9/2) and F-4(9/2) separately came from three-photon and two-photon processes. The decrease of n was well explained by the mechanism of competition between linear decay and upconversion processes for the depletion of the intermediate excited states.