Different additives such as barite, calcium carbonate, hematite, and ilmenite having high-density and fine solid materials are used to increase the density of drilling fluids. However, some of the weighting additives can cause some serious drilling problems such as barite (particle settling, formation damage, erosion, and insoluble filter cake). In this study and for the first time, anhydrite (calcium sulfate) is used as a weighting additive in the drilling fluids. Several laboratory experiments such as density, rheology, fluid loss, resistivity, and pH were carried out to assess the performance of calcium sulfate as a weighting additive in the drilling fluids. The performance of calcium sulfate as a weighting additive was compared with the commonly used weight enhancing additive calcium carbonate. The results showed that calcium sulfate has higher solubility than calcium carbonate. The fluid loss test showed that both additives lost the same volume of fluid and created the same thickness of filter cake; however, the solubility of calcium sulfate-based filter cake with organic and inorganic acids was higher compared with other weighting materials. Calcium sulfate-based filter cake was completely dissolved using a new formulation that consists of glutamic-diacetic acid (GLDA) chelating agent and potassium carbonate as a convertor. The removal efficiency after 10 h reached 100% in 20 wt% GLDA and 10 wt% potassium carbonate solution at 100 °C.