This paper considers the initial-boundary value problem of the Caputo time-fractional three-dimensional primitive equations for oceanic and atmospheric. Referring to Cao-Titi (Ann. of Math. 245-267, 2007), we consider the results of time-fractional case and obtain the global well-posedness of time-fractional primitive equations. It is proved that the well-posedness of the time fractional atmospheric ocean equation is still valid.