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Biomedical data analysis has been playing an important role in healthcare provision services. For decades, medical practitioners and researchers have been extracting and analyse biomedical data to derive different health-related information. Recently, there has been a significant rise in the amount of biomedical data collection. This is due to the availability of biomedical devices for the extraction of biomedical data which are more portable, easy to use and affordable, as an effect technology advancement. As the amount of biomedical data produced every day increases, the risk of human making analytical and diagnostic mistakes also increases. For example, there are approximately 40 million diagnostic errors involving medical imaging annually worldwide, hence rise a need for the development of fast, accurate, reliable and automatic means for analysis of biomedical data. Conventional machine learning has been used to assist in the analysis and interpretation of biomedical data automatically, but always limited with the need for feature extraction process to train the built models. To achieve this, three studies have been conducted. Two studies were conducted by using EEG signals and one study by using microscopic images of cancer cells. In the first study with EEG signals, our method managed to interpret motor imaginary activities from a 64 channels EEG device with 99% classification accuracy when all the 64 channels were used and 91.5% classification when the number of channels was selected to eight (8) channels. In a second study which involved steady-state visual evoked potential form of EEG signals, our method achieved an average of 94% classification accuracy by using two channels, skin like EEG sensor. In the third study for authentication of cancer cell lines by using microscopic images, our method managed to attain an average of 0.91 F1-score in the authentication of eight classes of cancer cell lines. Studies reported in this thesis, significantly shows that CNN can play a major role in the development of a computerised way in the analysis of biomedical data. Towards provision of better healthcare by using CNN in analysis of different formats of biomedical data, this thesis has three major contributions, i) introduction of a new method for EEG channels selection towards development of portable EEG sensors for real-life application, and ii) introduction of a method for cancer cell lines authentication in the laboratory environment towards development of anti-cancer drugs, and iii) Introduction of a method for authentication of isogenic cancer cell lines.