The up-conversion processes due to the continuous wave excitation of the holmium I-5(4) multiplet in LiYF4 crystal are investigated. Despite a very low absorption cross-section for the transition from the holmium I-5(8) ground state to the I-5(4) multiplet, a bright green up-converted emission originating from the S-5(2) multiplet is observed. The excitation and excited state absorption spectra indicate that the up-conversion process is based mainly on excited state absorption from the metastable I-5(7) multiplet, Some features of the up-converted green emission are characteristic for the photon avalanche process.