I am working CY8CKIT-001 DVK with CY8C55 Family processor module.In this how can we find the peak current, average current,taken by the board.
A quick and dirty method is with a DSO and a 1 ohm resistor in power lead.
Set DSO up for infinite persistance, and look at V drop across R, that will give you peak.
Now set DSO up to average its input channels, and look again at drop across R.
Hall effect another approach -
If you happen to have a multimeter with logging capability, use the approach with the 1Ohm resistor (or a larger one if you maximum current is lower than say 100mA). You can then use a spreadsheet (or whatever software the multimeter brings with it) to calculate what you need.