The Kumaraswamy distribution is a continuous model with broad applications in many areas, such as environment, medicine, and finance. The present study proposes a new compound continuous distribution named the odd beta prime-Kumaraswamy (OBPK) distribution. The proposed distribution is an extension of the Kumaraswamy distribution by incorporating the odd beta prime generalized family of distributions from T-X family. Various statistical properties of the OBPK distribution were derived. This distribution can be unimodal, and its shape is right-skewed or left-skewed. We employed the maximum likelihood estimation method to estimate the model parameters. The application of the new OBPK distribution is illustrated by applying two real-life data sets concerning the COVID-19 mortality rate during different periods, and its performance is compared with other well-known extended versions of the Kumaraswamy distribution. The adequacy of the new OBPK model is verified based on various statistical metrics. The findings indicate that the OBPK model outperforms other competitive models by providing the best fit to the COVID-19 data sets. This study updates the traditional Kumaraswamy distribution and provides a vital tool for modeling various phenomena in different domains.