A clearance adjusting apparatus disposed in front of a compressor of a gas turbine to axially move a compressor disk back and forth to adjust a tip clearance formed between a compressor blade and a compressor casing is provided. The clearance adjusting apparatus includes a hollow fastening part disposed in front of the compressor casing, a shaft disposed in the fastening part and coupled to a front side of the compressor disk, an adjusting part disposed between the fastening part and the shaft to axially move the shaft back and forth to adjust the tip clearance, and a biasing part disposed on the fastening part to bias the adjusting part back and forth to adjust a position of the adjusting part and the shaft.