By analyzing the data collected at the center-of-mass energy E-cm=3.773 GeV and below the D (D) over bar meson pair production threshold with the BES-II detector at the BEPC Collider, we directly measured the observed non-D (D) over bar cross section of psi(3770) decay to be sigma(obs)(psi(3770)-> non-D (D) over bar)=(0.95 +/- 0.35 +/- 0.29) nb at E-cm=3.773 GeV, and the branching fraction BF[psi(3770)-> non-D (D) over bar]=(13.4 +/- 5.0 +/- 3.6)% for inclusive non-D (D) over bar decay of psi(3770). We also determined the cross section for D (D) over bar meson pair production to be sigma(obs)(D (D) over bar)=(6.12 +/- 0.37 +/- 0.23) nb at E-cm=3.773 GeV.