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Abstract In the paper, we calculate the fragmentation functions for g → B c and g → B c ∗ $$ {B}_c^{\ast } $$ . The ultraviolet divergences in the calculation are removed through the renormalization of the operator definition of the fragmentation functions under the modified minimal subtrac- tion scheme. We then obtain the fragmentation functions D g → B c $$ {D}_{g\to {B}_c} $$ (z, μ F ) and D g → B c ∗ $$ {D}_{g\to {B}_c^{\ast }} $$ (z, μ F ), which are presented as figures and fitting functions. The obtained fragmentation functions are complementary to the previous work on the next-to-leading order fragmentation functions for b ¯ $$ \overline{b} $$ → B c ( B c ∗ $$ {B}_c^{\ast } $$ ) and c → B c ( B c ∗ $$ {B}_c^{\ast } $$ ).