We present a meta-algorithm for learning a posterior-inference algorithm for restricted probabilistic programs. Our meta-algorithm takes a training set of probabilistic programs that describe models with observations, and attempts to learn an efficient method for inferring the posterior of a similar program.A key feature of our approach is the use of what we call a white-box inference algorithm that analyses the given program sequentially using multiple neural networks to compute an approximate posterior.The parameters of these networks are learnt from a training set by our meta-algorithm.We empirically demonstrate that the learnt inference algorithm generalises well to programs that are new in terms of both parameters and model structures, and report cases where our approach achieves greater test-time efficiency than alternatives such as HMC.