The quality of ultrasound (US) images for the obstetric examination is crucial for accurate biometric measurement. However, manual quality control is a labor intensive process and often impractical in a clinical setting. To improve the efficiency of examination and alleviate the measurement error caused by improper US scanning operation and slice selection, a computerized fetal US image quality assessment (FUIQA) scheme is proposed to assist the implementation of US image quality control in the clinical obstetric examination. The proposed FUIQA is realized with two deep convolutional neural network models, which are denoted as L-CNN and C-CNN, respectively. The L-CNN aims to find the region of interest (ROI) of the fetal abdominal region in the US image. Based on the ROI found by the L-CNN, the C-CNN evaluates the image quality by assessing the goodness of depiction for the key structures of stomach bubble and umbilical vein. To further boost the performance of the L-CNN, we augment the input sources of the neural network with the local phase features along with the original US data. It will be shown that the heterogeneous input sources will help to improve the performance of the L-CNN. The performance of the proposed FUIQA is compared with the subjective image quality evaluation results from three medical doctors. With comprehensive experiments, it will be illustrated that the computerized assessment with our FUIQA scheme can be comparable to the subjective ratings from medical doctors.