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Neutron source has broad application prospects in crystallography, neutron irradiation, neutron therapy for cancer, and so on. As a new scheme to produce bright pulsed neutron source, the laser-driven neutron has attracted wide interest. In recent years, laser driven neutron sources have been extensively studied and the great progress has been made. Short pulsed laser driven neutron sources could be a compact and relatively cheap way to produce quasi-monoenergetic neutrons. The yields and the angular distributions of the laser-driven neutron sources are important in the research of laser-driven neutron sources and relevant applications. We conduct experimental investigation of this respect by using the XingGuang-Ⅲ high intense laser facility, which delivers synchronized picosecond and nanosecond laser pulses. The picosecond laser energy is 100 J, the pulse width is 1 ps, and the focusing spot diameter is 20 μm. At this time, the corresponding laser power density reaches 3×1019 W/cm2. A high-energy deuterium ion beam is produced by focusing the picosecond laser on a deuterated polyethylene foil, and the deuterium ion beam is incident on a secondary deuterated polyethylene planar target to activate the D-D reaction to obtain the neutron beam. In the experiment, the neutron yield and its angular distribution are measured by the different-sensitivity BD-PND bubble detectors, which are placed in the target chamber around the target. The emission of the neutron beam is found to be non-uniform. A maximum intensity of 5.13×107 n/sr is observed in the forward direction. The angular distribution of the neutron beam is theoretically calculated by taking into account the energy-angle cross section, the angular and energy distribution of the incident deuterium ion beam. The probability of the neutron energy-angle distribution in the laboratory system is obtained by the coordinate transformation from the probability in the center of mass frame. The results show good agreement with the experimental measurements. This experiment has a certain reference value in the practical application of D-D reaction neutron source.