Efforts performed in poverty alleviation by Islamic banking and financial institutions in terms of empowering the core poor in the society have been hampered by many constraints. As a result, the core poor are still being financially excluded. This paper attempts to explore constraints faced by Islamic Banking and suggests setting up a new integrative Islamic Financial Institution which could perform the ‘desired' shari'ah mission, i.e. to alleviate poverty as one of the main objectives of maqasid shari'ah. The method used here is exploratory analysis to identify problems and come up with the solution. It is found that there are several hindrances for Islamic Banking and Financial system internally and externally to perform poverty alleviation. Internally, the driven profit mission of these institutions, the fractional reserve system, lack of financial support from government to support the core poor and business failures, and the lack of sufficient social capital improvement, while externally; the lack of political will, lack of sufficient financial regulation and framework for dealing in shari'ah court, the use of paper currency only and the inflationary system, and less integrated system with Baitulmal institution.