In this paper, motivated by [Y. Wang and Z. Zhang, Ann. Inst. H.
Poincaré C Anal. Non Linéaire, 38(2021), 1989-2004], we study the
global C ∞ regularity of the two-dimensional steady compressible Prandtl
equations in the case of the favorable pressure gradient. The proof is
based on the maximum principle and interior a priori estimates.