A multi-arm polyethylene glycol derivative having a narrow molecular weight distribution represented by the formula (1): wherein, L represents a group selected from a linear or branched alkylene, arylene, or cycloalkylene group having two or more carbon atoms and combinations thereof, which may have an ether bond in a chain; X represents a dehydroxylation residue of a linear sugar alcohol having 5 or 7 carbon atoms; m is the number of polyethylene glycol chains bonded to X and represents 4 or 6; n is the average addition molar number of oxyethylene groups and represents an integer of 3 to 600; Y represents a single bond or an alkylene group as further defined herein; and Z represents a chemically reactive functional group.