In this contribution, an adaptive autoregressive model is proposed and developed to predict global ionospheric vertical total electron content maps (VTEC). Specifically, the spherical harmonic (SH) coefficients are predicted based on the autoregressive model, and the order of the autoregressive model is determined adaptively using the F-test method. To test our method, final CODE and IGS global ionospheric map (GIM) products, as well as altimeter TEC data during low and mid-to-high solar activity period collected by JASON, are used to evaluate the precision of our forecasting products. Results indicate that the predicted products derived from the model proposed in this paper have good consistency with the final GIMs in low solar activity, where the annual mean of the root-mean-square value is approximately 1.5 TECU. However, the performance of predicted vertical TEC in periods of mid-to-high solar activity has less accuracy than that during low solar activity periods, especially in the equatorial ionization anomaly region and the Southern Hemisphere. Additionally, in comparison with forecasting products, the final IGS GIMs have the best consistency with altimeter TEC data. Future work is needed to investigate the performance of forecasting products using the proposed method in an operational environment, rather than using the SH coefficients from the final CODE products, to understand the real-time applicability of the method.