The present invention relates to a conjugate of a protein or peptide with a polyethylene glycol derivative having catechol, wherein the protein or peptide is mono-PEGylated at the N-terminal with the polyethylene glycol derivative, and to a preparation method thereof. According to the invention, the catechol-PEG derivative can be site-specifically conjugated with the N-terminal amine group of a protein or peptide, so that a homogeneous polyethylene glycol-protein or -peptide conjugate can be obtained in high yield. Unlike a prior art conjugate, the conjugate obtained according to the invention allows the decrease in the activity of the protein to be minimized without chemically modifying the protein, and thus the conjugate has an excellent pharmacological effect. Also, because the conjugate is homogeneous, the process for preparing the conjugate can be simplified. Moreover, the conjugate has uniform biological efficacy in vivo and shows strong resistance to hydrolysis and thus a long in vivo duration time. Accordingly, the conjugate has the effect of increasing the in vivo efficacy and stability of the protein drug.