  We propose a method utilizing edge current to observe Majorana fermions in
the surface Andreev bound state for the superfluid $^3$He A- and B-phases. The
proposal is based on self-consistent analytic solutions of quasi-classical
Green's function with an edge. The local density of states and edge mass
current in the A-phase or edge spin current in the B-phase can be obtained from
these solutions. The edge current carried by the Majorana fermions is partially
cancelled by quasiparticles (QPs) in the continuum state outside the superfluid
gap. QPs contributing to the edge current in the continuum state are
distributed in energy even away from the superfluid gap. The effect of Majorana
fermions emerges in the depletion of the edge current by temperature within a
low-temperature range. The observations that the reduction in the mass current
is changed by $T^2$-power in the A-phase and the reduction in the spin current
is changed by $T^3$-power in the B-phase establish the existence of Majorana
fermions. We also point out another possibility for observing Majorana fermions
by controlling surface roughness.
