For　addressing　the　approximate　optimal　control　problem　of　nonlinear　affine　systems　with　the　terminal　state　constraint　and　asymmetric　control　constraints,　the　constrained　receding-horizon　heuristic　dynamic　programming　(RH-HDP)　algorithm　is　established　in　this　article.　In　consideration　of　the　RH　mechanism　of　model　predictive　control　(MPC),　the　approximate　optimal　control　problem　based　on　the　HDP　algorithm　is　transformed　into　a　battery　of　subproblems.　Then,　the　terminal　state　constraint　related　with　the　current　prediction　horizon　is　considered　such　that　the　terminal　state　is　forced　into　the　neighborhood　of　the　system　equilibrium　point.　In　addition,　the　asymmetric　control　constraints　are　introduced　to　release　the　pressure　of　actuator　saturation,　so　that　the　control　input　is　well　confined　within　the　given　constraint　range.　Meanwhile,　relevant　results　of　the　stability　proof　are　also　displayed　based　on　the　Lyapunov　approach.　Finally,　the　constrained　RH-HDP　algorithm　has　been　applied　in　two　kinds　of　systems　to　verify　its　effectiveness.　Comparative　experiments　with　the　traditional　HDP　algorithm　have　been　carried　out　to　verify　the　superiority　of　the　present　algorithm.