We present point-contact spectroscopy data for junctions between a normal metal and the newly discovered F-doped superconductor LaO$_{0.9}$F$_{0.1-\delta}$FeAs (F-LaOFeAs). A zero-bias conductance peak was observed and its shape and magnitude suggests the presence of Andreev bound states at the surface of F-LaOFeAs, which provides a possible evidence of an unconventional pairing symmetry with a nodal gap function. The maximum gap value $\Delta_0\approx3.9\pm0.7$meV was determined from the measured spectra, in good agreement with the recent experiments on specific heat and lower critical field.