Recent empirical work has considered the prediction of inflation by combining the information in a large number of time series. One such method that has been found to give consistently good results consists of simple equal weighted averaging of the forecasts over a large number of different models, each of which is a linear regression model that relates inflation to a single predictor and a lagged dependent variable. In this paper, I consider using Bayesian Model Averaging for pseudo out-of-sample prediction of US inflation, and find that it gives more accurate forecasts than simple equal weighted averaging. This superior performance is consistent across subsamples and inflation measures. Meanwhile, both methods substantially outperform a naive time series benchmark of predicting inflation by an autoregression.