The invention provides a process of recovering copper smelting waste acid and white smoke dusts. The process comprises the following steps: removing suspended particulate matters in the waste acid, regulating the acidity and the redox potential of the liquid, and enabling ions including molybdenum ions in the liquid to exist in a high positive ion mode; then selectively adsorbing rhenium by utilizing ion exchange resin, after adsorption is saturated, carrying out desorption to obtain a rhenate liquid, and carrying out concentration and crystallization to obtain rhenate; using the waste acid after adsorbing the rhenium for leaching the white smoke dusts; treating the white smoke dusts by adopting two segments of countercurrent acid leaching-chloride leaching process, recovering valuable metals including copper, zinc and cadmium of an acid leaching liquid, carrying out harmless treatment on harmful elements including arsenic by virtue of a molysite method, recovering valuable metals including bismuth of a chloride leaching liquid, and selling lead sulfate, serving as a main component of chloride leaching residues, to a lead smelting plant. According to the process provided by the invention, the rhenium in the waste acid can be efficiently separated and recovered, the leaching white smoke dusts of the waste acid can be fully utilized, and the waste acid and white smoke dust leaching liquids can be comprehensively treated by utilizing a set of copper recovering and arsenic harmless treatment system, so that the process matching ability is good, the comprehensive recovery rate of the valuable metals is high, the waste water treatment effect is good, the investment is little, the production cost is low, and the economical benefit is good.