Small and Medium Scale Enterprises (SMEs) in Nigeria are currently experiencing variety of cyber threats which is a big challenge as they are faced with wide range of cyber attacks that impact their businesses negatively. Challenges such as lack of access to finance, modern technology among others has hampered SMEs to perform their role as the engine growth in the economy. Despite the known challenges, most SMEs feels they are safe from cyber attacks than large organizations. However, something can be done for SMEs to at least prevent or mitigate these cyber attacks by addressing and understanding cyber security problems, developing good cyber culture and by creating a more proactive strategy that is suitable to SMEs. Therefore, firstly six known cyber security frameworks are thoroughly analyzed with the identified strengths and weaknesses. Subsequently, we propose a cyber security framework for SMEs in Nigeria that is dynamic, simple and cost effective, which is suitable to SMEs context.