This paper derives the best linear unbiased prediction (BLUP) for an unbalanced panel data model. Starting with a simple error component regression model with unbalanced panel data and random effects, it generalizes the BLUP derived by Taub (Journal of Econometrics, 1979, 10, 103–108) to unbalanced panels. Next it derives the BLUP for an unequally spaced panel data model with serial correlation of the AR(1) type in the remainder disturbances considered by Baltagi and Wu (Econometric Theory, 1999, 15, 814–823). This in turn extends the BLUP for a panel data model with AR(1) type remainder disturbances derived by Baltagi and Li (Journal of Forecasting, 1992, 11, 561–567) from the balanced to the unequally spaced panel data case. The derivations are easily implemented and reduce to tractable expressions using an extension of the Fuller and Battese (Journal of Econometrics, 1974, 2, 67–78) transformation from the balanced to the unbalanced panel data case.