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Data Centre (DC) has become a critical computing infrastructure that is essential to modern society by providing services such as cloud computing, Internet of Things (IoT) and big data. However, the cost of maintaining DC continues to rise as the demand for information technology services increase and this situation is further exacerbated in a country like Nigeria where there is highly unstable power supply from the national grid. The optimization of energy consumption in cloud computing DC using Genetic Algorithm (GA) to minimize the consumption of energy thereby extending network lifespan was one of the techniques used for optimization of power consumption. But the optimization was carried out with the assumption that all the parts of the modular server that are not carrying traffic is on idle mode and not completely off which consumes extra power compare to when it is completely off. Therefore, this work proposed optimization of power consumption utilization in a cloud computing DC using Kalman Filter (KF) with GA. Historical consumption trend and network traffic is analyzed to reduce the amount spent on power with assumption that servers in the DC operate as modular units which can be powered separately as required, in contrast to keeping entire servers always powered. Data from five different servers were collected from MTN Abuja DC in Nigeria. The servers were named BSC 13, BSC 14, BSC 15, RNC 05 and RNC 06. These consist of data recorded for two year-5th January to 30th December 2019 as well as 5th January to 31st December 2020. The GA optimizer is used to obtain the best possible values for the Kalman Filter (KF) parameters. Then, the KF model is used to predict the future power consumption value on hourly basis for each day of the week. The proposed model gives low power consumption with accurate prediction when compared with the existing models.