In this paper a new speckle reduction method for multi-polarisation Synthetic Aperture Radar (SAR) is proposed by using a constrained-variational model. Variational method is a new technique for SAR speckle removal. In this paper, we generalize the variational method from single-polarisation SAR into multi-polarisation SAR. For a given multi-polarisation SAR, we could define an energy functional. The energy evolves as the original image changes. When the energy reaches its minimum, the corresponding image is regarded as the desired result. In each channel of the multi-polarisation SAR, the speckle follows a Gamma law with mean μ = 1 and variance σ2 = 1/M for M-look SAR. This statistical information is used to construct the energy functional. Our energy is a regularization term, which is the integral for the norm of image gradient, with constraints coming from each channel. Then we use the variational method and heat flow method to obtain the minimizer of the energy. A three-intensity image (|HH|2, |HV|2 and |VV|2) is used to demonstrate our algorithm. Numerical experiment shows a promising result.