The success of an e-learning system depends largely on the acceptance and use that teachers give this tool. After critically evaluate models of technology adoption, including the Technology Acceptance Model (TAM) and TAM2, we built a conceptual model to predict the level of acceptance and use of elearning system among teachers. This model extends TAM2 and includes technical support, computer self-efficacy, social influence, perceived enjoyment and satisfaction. Data were collected from 145 teachers of a University in Ecuador. For data collection, a form in Likert scale was sent by email. Upon receipt of the data, these missing data reported 4.2%, to correct this data imputation method it was applied for replacement by mean. After performing the checks about satisfactory reliability and validity, the structural model was tested using PLS. The results indicate that perceived ease of use and perceived usefulness have a direct effect on the intension of using e-learning systems. Perceived enjoyment, perceived ease of use and social influence have a direct effect on the perceived usefulness. Perceived enjoyment and computer self-efficacy both have a direct effect on perceived ease of use of e-learning systems. Universities Principals should not only worry about the basic design of e-learning systems, but also explicitly address individual differences among teachers using elearning system.