In Vietnam, there are a huge number of quarries that are exploited and mainly provide materials to the construction sector of the country. However, most of the quarries are operating without topographic plans due to a lack of surveying activities. This paper introduces an approach of using low-cost UAVs to produce digital surface models which in turn are used to draw topographic maps of quarries in Vietnam. For assessments of accuracy, safety, and working efficiency, four quarries different in terrain conditions, namely Luong Son, Long Son, Nui Nho, and Nui Dai were selected as the study areas. Ground control points were established in each area by using GNSS/RTK for camera calibration and accuracy assessment. The accuracy of DSM was assessed using the root-mean-square error (RMSE) in X, Y, Z, XY, and XYZ components. Capturing images from each site were processed by using Agisoft®PhotoScan Professional 1.5.2. The results showed that all the DSM models of the four areas have high accuracy, RMSE on the checked GCPs ranges from 1.0 to 9.0 cm, from 1.2 to 5.0 cm, from 4.4 to 13.4 cm, from 1.6 to 10.3 cm, and from 4.9 to 16.9 cm for X, Y, Z, XY, XYZ components, respectively. We concluded that the low-cost UAV based mapping technology can guarantee the accuracy of DSMs, the safety of UAV flying, and the efficiency of surveying working simultaneously when using in quarries.