Properties of copolymers are generally influenced by the structure of the monomers and polymers. For the purpose of understanding the effect of polymer structure on the properties, two kinds of copolymers, poly(3,4-dihydroxyphenylalanine)-g-polylactide and poly(3,4-dihydroxyphenylalanine)-b-polylactide (PDOPA-g-PLA and PDOPA-b-PLA) were designed and prepared by ring-opening polymerization of lactide with pre-prepared PDOPA as the initiator and the amidation of the functional PLA and PDOPA oligomer, respectively. The molecular weight and composition of the copolymers could be adjusted by changing the molar ratio of LA and DOPA and were confirmed by gel permeation chromatography (GPC) and proton nuclear magnetic resonance (1H NMR) spectra. The obtained copolymers with graft and block structures showed high solubility even in common organic solvents. The effects of the graft and block structures on the thermal and degradation properties were also detected. The PDOPA-g-PLA copolymers showed higher thermal stability than the PDOPA-b-PLA copolymers, due to the PDOPA-g-PLA copolymers with regular structure and strong π-π stacking interactions among the intermolecular and intramolecular chains. In addition, the degradation results showed that the PDOPA-g-PLA copolymers and the copolymers with higher DOPA composition had quicker degradation speeds. Interestingly, both two kinds of copolymers, after degradation, became undissolved in the organic solvents because of the oxidation and crosslinking formation of the catechol groups in the DOPA units during degradation in alkaline solution. Moreover, fluorescent microscopy results showed good biocompatibility of the PDOPA-g-PLA and PDOPA-b-PLA copolymers. The PDOPA and PLA copolymers have the potential applications to the biomedical and industrial fields.