To build advanced all solid-state LiDAR, optical phased arrays (OPAs) with a large field of view are highly desirable. As a critical building block, a wide-angle waveguide grating antenna is proposed here. Instead of aiming at the elimination of downward radiation of waveguide grating antennas (WGAs) to improve efficiencies, we in turn utilize the downward radiation and double the range of beam steering. In addition to widened field of views, the steered beams in two directions come from a common set of power splitters, phase shifters and antennas, which greatly reduces chip complexity and power consumption, especially for large-scale OPAs. Beam interference and power fluctuation in the far field due to downward emission can be decreased by specially designed SiO2/Si3N4 antireflection coating. The WGA exhibits balanced emissions in both the upward and downward directions, in which the field of view in each direction is more than 90°. The normalized intensity remains almost the same with a small variation of 10% from -39° to 39° for the upward emission and from -42° to 42° for the downward emission. This WGA is featured by a flat-top radiation pattern in far field, high emission efficiency and good tolerance to device fabrication errors. It holds good potential to achieve wide-angle optical phased arrays.