As　an　emerging　computing　paradigm,　Mobile　Edge　Computing　(MEC)　significantly　enhances　user　experience　and　alleviates　network　congestion　by　strategically　deploying　edge　servers　in　close　proximity　to　mobile　users.　However,　the　effectiveness　of　MEC　hinges　on　the　precise　placement　of　these　edge　servers,　a　critical　factor　in　determining　the　Quality　of　Experience　(QoE)　for　mobile　users.　While　existing　studies　predominantly　focus　on　optimizing　edge　server　placement　in　static　scenarios,　they　often　fall　short　when　faced　with　user　mobility,　resulting　in　a　degradation　of　QoE.　To　address　this　challenge,　we　propose　an　adaptive　edge　server　placement　approach　that　leverages　Deep　Reinforcement　Learning　(DRL)　to　select　the　base　stations　for　placing　edge　servers　in　a　dynamic　MEC　environment.　Our　objective　is　to　minimize　access　delay　by　optimizing　edge　server　placement　for　adapting　to　dynamic　environment.　To　tackle　the　vast　action　space　associated　with　edge　server　placement,　we　introduce　a　novel　activation　function　in　the　actor　neural　network　for　efficient　exploration.　Furthermore,　to　enhance　the　adaptability　of　the　derived　edge　server　placement　strategy,　we　meticulously　design　a　new　reward　function,　which　takes　into　account　the　minimization　of　total　access　delay　within　dynamic　MEC　scenarios.　Finally,　to　validate　the　effectiveness　of　our　proposed　method,　extensive　experiments　were　conducted　using　the　Shanghai　Telecom　dataset.　The　results　demonstrate　that　our　approach　outperforms　baseline　methods　in　minimizing　access　delay　for　users　in　dynamic　MEC　scenarios.