Fruit growth across various stages of development determines the extent of final fruit size, and is therefore of high economic value. The two main processes that mediate growth, cell production and cell expansion, contribute differentially to growth across various stages of fruit development. In apple, growth during early fruit development is largely facilitated by cell production. Mid and late stages of fruit development display growth mediated mostly by cell expansion. Mechanisms that regulate these processes and consequently the growth rates of fruit are not well understood. The objective of this study was to determine the molecular processes associated with higher relative growth rates (RGR) in the apple fruit during different stages of development. To address this objective, we exploited the inherent natural variation in RGR within a population of ‘Empire’ fruit. These evaluations were performed during early and mid-fruit development stages. At each stage, change in fruit size (volume) was determined across a 4 d interval to obtain the RGR. The population of fruit was grouped into two classes based on their RGR values: High and Low RGR. RNA-sequencing analyses were performed to compare the transcriptomes of the two classes of fruit. During early fruit development, the High RGR class fruit displayed 1.46-fold greater growth rates than the Low RGR fruit. Transcriptome analysis indicated that genes associated with cell division processes such as HISTONES, CYCLINS and CYCLIN DEPENDENT KINASES were more abundant in fruit with higher RGR. During mid-fruit development, fruit displayed relatively lower RGR. Yet the High and Low RGR fruit classes differed by 1.76-fold. However, only a limited set of genes, mostly associated with oxidation-reduction processes, were differentially expressed across these two groups. Overall, these data suggest that processes that regulate cell division control the growth rates of apple fruit during early fruit development.