Atypical fetal chromosomal anomalies are more frequent than previously recognized and can affect fetal development. We propose a screening strategy for a genome-wide non-invasive prenatal test (NIPT) to detect these atypical chromosomal anomalies (ACAs). Two sample cohorts were tested. Assay performances were determined using Cohort A, which consisted of 192 biobanked plasma samples—42 with ACAs, and 150 without. The rate of additional invasive diagnostic procedures was determined using Cohort B, which consisted of 3097 pregnant women referred for routine NIPT. Of the 192 samples in Cohort A, there were four initial test failures and six discordant calls; overall sensitivity was 88.1% (37/42; CI 75.00–94.81) and specificity was 99.3% (145/146; CI 96.22–99.88). In Cohort B, there were 90 first-pass failures (2.9%). The rate of positive results indicating an anomaly was 1.2% (36/3007) and 0.57% (17/3007) when limited to significant unbalanced chromosomal anomalies and trisomies 8, 9, 12, 14, 15, 16, and 22. These results show that genome-wide NIPT can screen for ACAs with an acceptable sensitivity and a small increase in invasive testing, particularly for women with increased risk following maternal serum screening and by limiting screening to structural anomalies and the most clinically meaningful trisomies.