In　this　paper,　a　value-iteration-based　off-policy　Q-learning　algorithm　is　developed.　The　proposed　algorithm　solves　the　optimal　regulation　problem　of　nonlinear　systems　with　unknown　dynamics.　Under　the　off-policy　mechanism,　the　algorithm　utilizes　the　behavioral　policy　for　full　exploration,　which　is　beneficial　to　avoid　the　target　policy　from　falling　into　the　local　optimal　solution.　In　addition,　a　relaxation　factor　is　introduced　to　adjust　the　convergence　rate　of　the　cost　function　sequence.　To　implement　the　algorithm,　the　critic　network　and　the　action　network　are　used　to　approximate　the　optimal　Q-function　and　the　optimal　control　policy,　respectively.　Finally,　a　simulation　example　is　presented　to　demonstrate　the　effectiveness　of　the　proposed　algorithm.　©　2024　IEEE.