With the evolution and adaptability of 3G telecommunication features on handheld devices, education tends to go out of conventional campus into a feat where teaching and learning could be ubiquity, convenient, location independent and personalized. The rapid growth of mobile users will push educational institutions to adopt mobile learning solution. We propose and verify a theoretical framework of university students’m-learning acceptance and intention to use, based mainly on the Technology Acceptance Model (TAM). A sample of 458 university students took part in this research. The structural equation modeling techniques are employed to explain the adoption processes of hypothesized research model. A theoretical general framework TAMM is developed based on TAM. Our result proved that psychometric constructs of TAM can be extended and that TAMM is well suited, and of good theoretical tool in understanding users’ acceptance of mobile learning in south west part of Nigeria. Mobile learning self-efficacy is the most importance construct influencing behavioral intention to use m-learning with path co-efficient of 0.77 and t-value of 1.76* at p< 0.05 which is significant. Self efficacy is able to explain the highest percent of the variance (70) observed in behavioral intention to use m-learning in south-west part of Nigeria.