The invention discloses a continuous ion exchanging device for extracting lithium and a lithium extraction process. The continuous ion exchanging device for extracting lithium comprises a running base and a plurality of adsorbing columns; the running base comprises an adsorption region, a drip washing region and a desorption region; the plurality of adsorbing columns are arranged on the running base and are distributed in the adsorption region, the drip washing region and the desorption region; the adsorbing columns in the adsorption region communicate with a raw material liquid charging pipe; the adsorbing columns in the drip washing region communicate with a drip washing liquid charging pipe; the adsorbing columns in the desorption region communicate with a desorption liquid charging pipe; and the positions of the absorption region, the drip washing region and the desorption region on the running base are successively replaced. The lithium extraction process adopts the continuous ion exchanging device; with the passage of time and the operation of the running base, the absorption region, the drip washing region and the desorption region on the running base separately implement adsorption operation, drip washing operation and desorption operation; all regions are continuously and alternately replaced so that the overall lithium extraction operation can be quickly and continuously implemented, and thus the lithium extraction efficiency and the comprehensive development and utilization efficiency of resources are improved.