  We use an idea of Wang and Yau to give a new definition of quasi-local mass
for a topological sphere in an initial date set. The new definition modifies
Brown-York's definition by using certain spinor norm as lapse function. And it
requires mean curvature of the topological sphere satisfies apparent horizon
conditions, the topological sphere can be isometrically into Euclidean 3-space
and mean curvature of the initial date set does not change sign. The positivity
holds if we further assume the image of the topological sphere in Euclidean
3-space has nonnegative mean curvature.
