A number of high-entropy alloys (HEAs) in the TiVZrNbHf system have been synthesized by arc melting and systematically evaluated for their hydrogen sorption characteristics. A total of 21 alloys with varying elemental compositions were investigated, and 17 of them form body-centered-cubic (bcc) solid solutions in the as-cast state. A total of 15 alloys form either face-centered-cubic (fcc) or body-centered-tetragonal (bct) hydrides after exposure to gaseous hydrogen with hydrogen per metal ratios (H/M) as high as 2.0. Linear trends are observed between the volumetric expansion per metal atom [(V/Z)fcc/bct - (V/Z)bcc/hcp]/(V/Z)bcc/hcp with the valence electron concentration and average Pauling electronegativity (χp) of the alloys. However, no correlation was observed between the atomic size mismatch, δ, and any investigated hydrogen sorption property such as the maximum storage capacity or onset temperature for hydrogen release.