Asian option pricing is difficult because the underlying average does not have a well known distribution. For large averaging times, the distribution and option price do have known limiting forms but perversely, Asian options are more difficult to price the shorter and less volatile the situation. Moreover floating strike options are more difficult to price than fixed strike because a joint distribution is required in the former. In this paper we provide an efficient method for floating strike options that works well for the low and medium volatility as well a finite maturity cases, because the method is based on the first few terms only of a series expansion of the underlying variable in volatility. As well as complementing other numerical techniques our method is fast and efficient compared to the Monte Carlo benchmark method adopted.