Aiming at the problem of the existing drift detection methods in balancing the detection delay， false positives， false negatives， and spatiotemporal efficiency， a new stage transition threshold parameter was proposed， and a multi-stage weighting mechanism including “stable stage-warning stage-drift stage” was introduced in the concept drift detection to weight the instances in stages， and the mechanism was applied to the double sliding window. Then a Multi-Stage weighted Drift Detection Method （MSDDM） based on Hoeffding inequality was proposed. On artificial datasets， MSDDM detected abrupt and gradual concept drift faster than Fast Hoeffding Drift Detection Method （FHDDM）， Drift Detection Method based on Hoeffding’s bound （HDDM） and other drift detection methods， while maintained a low false detection rate and a false alarm rate. At the same time， MSDDM had the highest classification accuracy in most cases compared with other methods on real-world datasets. Experimental results show that MSDDM can detect concept drift in data streams with high drift detection performance and great spatiotemporal efficiency.