Placement　and　routing　are　two　key　problems　in　VLSI　physical　design.　However,　there　may　be　out　of　sync　between　the　two　problems　with　congestion　and　routing　resources.　Therefore,　it　is　desirable　to　design　an　efficient　and　highly　coupled　placement　and　routing　engine.　This　paper　proposes　an　incremental　3D　global　routing　engine　considering　cell　movement　and　complex　routing　constraints　to　relocate　cells　and　reroute　nets.　We　develop　an　efficient　movement　evaluation　method　to　find　desired　locations　and　estimated　routing　resources　for　each　cell.　Then,　we　adopt　an　iterative　approach　to　move　cells　to　reduce　routing　resources.　To　reduce　the　time　consumption　of　rerouting,　we　propose　two　technologies　(searching　space　reduction　and　data　structure　optimization)　to　speed　up　the　rerouting　process.　Compared　with　the　participating　teams　at　the　2020　CAD　Contest　at　ICCAD　based　on　the　contest　benchmarks,　experiment　results　show　that　our　proposed　algorithm　achieves　the　best　runtime　and　routing　resources　while　satisfying　all　the　routing　constraints.