  It is known that sectional-hyperbolic attracting sets, for a $C^2$ flow on a
finite dimensional compact manifold, have at most finitely many ergodic
physical invariant probability measures. We prove an upper bound for the number
of distinct ergodic physical measures supported on a connected
singular-hyperbolic attracting set for a $3$-flow. This bound depends only on
the number of Lorenz-like equilibria contained in the attracting set. Examples
of singular-hyperbolic attracting sets are provided showing that the bound is
sharp.
