Sorghum is a major cereal crop that plays an important role in food security for millions of people in arid and semi-arid regions, but its production is threatened by drought. Therefore, understanding the genetic basis of transpiration rate during the early development stage is a key step towards improving sorghum production. The objectives were to study the physiological mechanisms for water-saving in sorghum under non-limiting water conditions and to map QTL related to leaf transpiration along with root and plant morphology traits. We phenotyped 177 recombinant inbred lines derived from a cross between CSM63E and 93B1057 in plastic pots, under semi-controlled conditions using a randomised complete block design (RCBD) with four replications. Results showed a wide range of phenotypic variation in the RIL population. The broad-sense heritability ranged from 0.46 for leaf dry weight to 0.76 for plant height. We also reported a positive correlation between root (root dry weight, root volume, total number of nodal roots, root length and root area) and leaf (green leaf number, leaf dry weight and leaf area) traits. The transpiration rate traits were negatively associated with root and leaf traits, while there was a positive correlation with plant height. This study allowed the mapping of 23 QTLs on Chromosomes 1, 2, 3, 4, 6, 8 and 9, including seven QTLs for transpiration rate traits, five QTLs for root traits and seven QTLs for leaf and plant height traits. Additional studies can be conducted in drought conditions to identify more QTL associated with traits in sorghum.