The mass spectrum of stellar-mass black holes ( BHs ) is highly uncertain . Dynamical mass measurements are available only for few ( \sim { } 10 ) BHs in X-ray binaries , while theoretical models strongly depend on the hydrodynamics of supernova ( SN ) explosions and on the evolution of massive stars . In this paper , we present and discuss the mass spectrum of compact remnants that we obtained with SEVN , a new public population-synthesis code , which couples the PARSEC stellar evolution tracks with up-to-date recipes for SN explosion ( depending on the Carbon-Oxygen mass of the progenitor , on the compactness of the stellar core at pre-SN stage , and on a recent two-parameter criterion based on the dimensionless entropy per nucleon at pre-SN stage ) . SEVN can be used both as a stand-alone code and in combination with direct-summation N-body codes ( Starlab , HiGPUs ) . The PARSEC stellar evolution tracks currently implemented in SEVN predict significantly larger values of the Carbon-Oxygen core mass with respect to previous models . For most of the SN recipes we adopt , this implies substantially larger BH masses at low metallicity ( \leq { } 2 \times { } 10 ^ { -3 } ) , than other population-synthesis codes . The maximum BH mass found with SEVN is \sim { } 25 , 60 and 130 \textrm { M } _ { \odot } at metallicity Z = 2 \times { } 10 ^ { -2 } , 2 \times { } 10 ^ { -3 } and 2 \times { } 10 ^ { -4 } , respectively . Mass loss by stellar winds plays a major role in determining the mass of BHs for very massive stars ( \geq { } 90 M _ { \odot } { } ) , while the remnant mass spectrum depends mostly on the adopted SN recipe for lower progenitor masses . We discuss the implications of our results for the transition between NS and BH mass , and for the expected number of massive BHs ( with mass > 25 M _ { \odot } { } ) as a function of metallicity .