Polyesters containing functional groups are a suitable candidate matrix for cell culture in tissue engineering. Three types of semicrystalline copolymer poly(L-lactide-co-β-malic acid) [P(LA-co-BMD)] with pendent carboxyl groups were synthesized in this study. The functional monomer 3(S)-[(benzyloxycarbonyl)methyl]-1,4-dioxane-2,5-dione (BMD) was synthesized using L-aspartic acid. The copolymer P(LA-co-BMD) was then synthesized through ring-opening copolymerization of L-LA and BMD, with dodecanol as initiator and stannous octoate as catalyst. Copolymer structure was characterized by 1H nuclear magnetic resonance (1H NMR), gel permeation chromatography (GPC), and differential scanning calorimetry (DSC) analyses. Results of 1H NMR and GPC analyses showed that the copolymers were synthesized successfully. DSC curves showed that the crystal melting peak and enthalpy decreased with increased BMD. The crystallinity of the copolymer was destroyed by the presence of the functional monomer. After deprotection, carboxyl groups were coupled with the isoleucine-lysine-valine-alanine-valine peptide through N-hydroxysuccinimide/dicyclohexylcarbodiimide method. The small peptide was beneficial to the axon growth of PC12 cells.