A PEGylated (polyethylene glycolated) insulin lispro compound of the formula: P-[(a)-(B)], wherein: A is the A-chain of insulin lispro (SEQ ID NO: 1) B is the B-chain of insulin lispro (SEQ ID NO: 3) and P is a PEG having a molecular weight in the range from about 17.5 kDa to about 40 kDa. A and B are cross-linked and P is attached via a urethane covalent bond to the epsilon-amino group of the lysine at position 28 of B. The compound can be used to treat hyperglycaemia or diabetes.