This work introduces a B-frame coding framework, termed B-CANF, that exploits conditional augmented normalizing flows for B-frame coding. Learned B-frame coding is less explored and more challenging. Motivated by recent advances in conditional P-frame coding, B-CANF is the first attempt at applying flow-based models to both conditional motion and inter-frame coding. B-CANF features frame-type adaptive coding that learns better bit allocation for hierarchical B-frame coding. B-CANF also introduces a special type of B-frame, called B*-frame, to mimic P-frame coding. On commonly used datasets, B-CANF achieves the state-of-the-art compression performance, showing comparable BD-rate results (in terms of PSNR-RGB) to HM-16.23 under the random access configuration.