The last decade has seen an unprecedented growth in the practice Of Islamic banking and finance which has now been recognized as a viable alternative and hopefully it will be the only financial system needed to get out from the current crisis, with the expectation that it will play an increasingly more important role in the years to come, as such, the appeal of this type of finance steams mainly from its underlying fundamental concept of justice as well as from the sharing of risk and prohibition of interest. The data used in this test were collected from 150 respondent. Five-point Likert type was used to obtain respondent's level of agreement. However the eligibility of 126 respondents, these rspondents were described according to gender, Surabaya domicile, age, customers of Bank Muamalat, registered as Bank Muamalat customers at least 1 year and Muslim. The Research finding that Bank Muamalat must work extensively to influece customer's buying desicion. and increase their credibility by paying attention on the accuracy of their compliance towards Islamic Banking rules and how to gain more trust from customers which will convince them that sharia banks are much better compared to the conventional bank