Understanding the genetic variability, heritability and genetic advance (GA) of traits in any plant population is an important pre-requisite for variety development. The objectives of the study were to assess the level of genetic variability among vegetative growth traits and yield, assess the relationship among the growth traits and yield and predict GA for the most heritable traits among Robusta coffee full-sib families. The trial was established in June 2009 at the experimental fields of the Cocoa Research Institute of Ghana with 62 full-sib families planted in a randomized complete block design with six replications. Significant (p < 0.05) variation was observed among the full-sib families evaluated for all traits, except for span (canopy diameter). Span and number of laterals were genetically correlated (p < 0.001) with cumulative yield (2013–2017), with span being the vegetative growth trait most strongly related to cumulative yield (rg = 0.60, p < 0.001). The most heritable vegetative growth and yield traits were, respectively, number of laterals (H2 = 0.59) and cumulative yield (H2 = 0.41). The top 10 families (BP40, BP41, BP9, BP36, BP34, BP28, BP37, BP14, BP4 and BP10) in terms of cumulative yield are proposed for multi-location evaluation and possible release as hybrids for coffee farmers in Ghana.