Low-grade flow energy possesses large reserve and wide distribution in environment, but is far from fully exploited due to high cost when using traditional rotary convertors. Flapping foil can effectively extract flow energy with large span-chord ratio at the low Reynolds number and, thus, may find its application in low-grade flow energy conversion. The motion profiles are the key factors that determine its energy extraction performance. Although massive works have been devoted to optimize its motion parameters, the limit of its performance is still not clear. We developed a more flexible method to describe its motion profile to further approach its theoretical limiting performance. It is demonstrated that the spline motion profile is so flexible that it can cover sinusoidal and some non-sinusoidal motion profiles. This flexibility provides the possibility of much more complicated profile shape and, thus, better energy extraction performance. The spline motion profile obtains 11% and 7% performance improvement compared to sinusoidal and other non-sinusoidal motions, respectively. We achieved a maximum efficiency of 37.3% with a spline controlled motion profile at a low Reynolds number of 1100. Although this efficiency is, indeed, not the limiting performance at this Reynolds number, this work provides a new method approaching the theoretical limiting performance.