The heavy reliance on digital technology, by individuals and organizations, has reshaped the traditional economy into a digital economy. In response, cybercriminals' attention has shifted dramatically from showing off skills and conducting individual attacks into high sophisticated attacks with financial gain as the goal. This, inevitably, poses a challenge to the cybersecurity community as they strive to find solutions to preserve the confidentiality, availability and integrity of the individual users' and corporates' private data and services. Cybercriminals mainly deploy malware to achieve their goals, which could be in the form of ransomware, botnets, etc. The use of encryption, packing and polymorphism techniques makes it harder to detect the malware files, especially when these are created in great numbers every day. In this paper, a novel framework, named Malware Spectrogram Image Classification (MSIC), is proposed. It employs spectrogram images in conjunction with the convolution neural network to classify a malware file to its corresponding family and to differentiate it from a benign file. Further, this research shares with the research community two privately collected labeled malicious and benign datasets. The evaluation of MSIC showed its effectiveness to be 91.6% F-measure and 92.8% accuracy in classifying malware files to their corresponding families, in comparison to, respectively, 90.6% and 92.3% results produced by the grayscale image classification approach. Likewise, in classifying files as malicious or benign, MSIC scored 96% F-measure and accuracy results compared to 95.5% with the grayscale solution. Also, MSIC required less computational time in converting and resizing the files than the grayscale framework.