We present the first analysis of three-dimensional genus statistics for the SDSS EDR galaxy sample . Due to the complicated survey volume and the selection function , analytic predictions of the genus statistics for this sample are not feasible , therefore we construct extensive mock catalogs from N-body simulations in order to compare the observed data with model predictions . This comparison allows us to evaluate the effects of a variety of observational systematics on the estimated genus for the SDSS sample , including the shape of the survey volume , the redshift distortion effect , and the radial selection function due to the magnitude limit . The observed genus for the SDSS EDR galaxy sample is consistent with that predicted by simulations of a \Lambda -dominated spatially-flat cold dark matter model . Standard ( \Omega _ { 0 } = 1 ) cold dark matter model predictions do not match the observations . We discuss how future SDSS galaxy samples will yield improved estimates of the genus .