Longitudinal data analysis has been widely employed to examine between-individual differences in within-individual changes. One challenge of such analyses is that the rate-of-change is only available indirectly when change patterns are nonlinear with respect to time. Latent change score models (LCSMs), which can be employed to investigate the change in rate-of-change at the individual level, have been developed to address this challenge. We extend an existing LCSM with the Jenss-Bayley growth curve and propose a novel expression for change scores that allows for (1) unequally spaced study waves and (2) individual measurement occasions around each wave. We also extend the existing model to estimate the individual ratio of the growth acceleration (that largely determines the trajectory shape and is viewed as the most important parameter in the Jenss-Bayley model). We present the proposed model by a simulation study and a real-world data analysis. Our simulation study demonstrates that the proposed model can estimate the parameters unbiasedly and precisely and exhibit target confidence interval coverage. The simulation study also shows that the proposed model with the novel expression for the change scores outperforms the existing model. An empirical example using longitudinal reading scores shows that the model can estimate the individual ratio of the growth acceleration and generate individual rate-of-change in practice. We also provide the corresponding code for the proposed model.