Cross flow fans are used in various applications, especially in industrial ventilation applications and in room air conditioners, due to their superior performance characteristics. Unlike radial and/or axial fans, the design of cross flow fans have been mostly based on earlier experiences and experiments. In the present study, numerical computations of flow fields through a cross flow fan used in room air conditioner are performed to investigate the detailed flow fields and to study the effect of the blade shape on performance curves to aid better design of the fan. Despite some discrepancies between the two results, it is seen from the present study that the computational results agree quite well with the qualitative experimental results. It is also shown from the present study that by having a different shape of blade, it is possible to achieve about $15\%$ increase in flow rates. The stimulating results of the present study can be used in the design of high performance cross flow fans with the use of optimal design algorithm and experimental verifications.