Analyzing the spatio-temporal growth of the built-up areas of any urban place is incredibly much vital for the proper planning and development of the urban areas. The present study emphasizes on determining the rate and pattern of spatio-temporal growth of Rangpur City Corporation (RpCC) for the year of 1989, 2000, 2010, and 2017 through Shannon's Entropy with the help of GIS and remote sensing techniques. The Shannon's Entropy technique was adopted in order to determining the dispersion or compactness in the pattern of the built-up areas in the study area. In the present study, Lands at Operational Land Imager (OLI), Lands at Thematic Mapper (TM) and Lands at Enhanced Thematic Mapper plus (ETM+) satellite images on the year of 1989, 2000, 2010, and 2017 were analyzed for certain interpretations. The changes of the built-up areas in RpCC were identified and determined through supervised classification using ArcMap10.5 software. The study indicated that spatio-temporal growth of the built-up areas have been in RpCC was existed during 1989-2017. The built-up areas increased by 5.89 Sq.km. during 1989 -2000, 32.23 Sq.km. during 2000- 2010 and 18.85 Sq.km. during 2010-2017 and the expansion rate of the built-up areas was 8.02%, 25.64% and 6.01% during 1989-2000, 2000-2010 and 2010-2017 respectively. The relative entropy value of 1989, 2000, 2010 and 2017 was found 0.17, 0.24, 0.47 and 0.53 which interprets that the expansion of the built-up areas was existed in RpCC and the pattern of expansion was dispersed. However, the outcomes of this study will be very helpful to formulate perfect planning and management system regarding the expansion of the built-up areas the built-up areas expansion of RpCC.