When employing bonded discrete element models (DEMs) to model rocks, a fundamental problem is how to determine the micro parameters to accurately simulate the rock strength characteristics. One promising way to improve calibration efficiency is to fully utilize the underlying relationship between DEM micro parameters and the macro strengths of rocks. This paper developed an analytical-optimal calibration framework to automatically determine DEM bond strength parameters. Extensive parametric analysis was first conducted to obtain the relationships between DEM micro-parameters and macro strengths. Bond tensile strength, cohesion and local internal friction angle were identified as independent variables for calibration. The automatic calibration method is divided into two stages. Firstly, the rough estimations of the bond tensile and cohesion were obtained by successively performing a direct tensile simulation test and a uniaxial compression simulation test, while the local internal friction angle was estimated by an empirical formula about the Hoek-Brown parameter m