A series of Er3+, Tm3+, Yb3+ co-doped or tri-doped SrLu2O4 phosphors were synthesized by a high-temperature solid-state reaction method. The crystal structure was characterized by X-ray diffraction technique and further validated by Rietveld refinement. The chemical composition and elemental distribution of tri-doped sample were determined by the energy-dispersive spectrometry. It is worthwhile to note that the upconversion (UC) luminescence of as-prepared samples could be precisely controlled by adjusting the Yb3+ doping concentration and the excitation pump power. A bright UC white light in Er3+/Tm3+/Yb3+ tri-doped SrLu2O4 samples was observed by controlling the intensities of red, green and blue emissions. Under various pump powers in the range of 290-810 mW, the color coordinates could be effectively tuned in a quite broad white region. Particularly, the color coordinate of optimal sample under 630 mW at 980-nm excitation is (0.3336, 0.3244), which is very close to the standard white light illumination (0.333, 0.333) and the corresponding correlated color temperature is 5442 K. Based on the UC emission spectra and luminescence decay curves, the energy transfer (ET) mechanisms involved in the different UC processes were proposed in detail. The results imply that ET processes of Yb3+ -> Er3+, Yb3+ -> Tm3+ and Tm3+ -> Er3+ worked simultaneously in tri-doped system and produced white UC emissions by means of two- or three-photon processes. The Er3+/Tm3+/Yb3+ tri-doped SrLu2O4 phosphor can be a potential candidate for white UC material in displays, backlights and white-light sources.