The short-pulse neutron source based on ultra-short and ultra-intense laser is an ideal neutron source for ultra-fast neutron detection. For many applications of the novel laser neutron source, the neutron yield now becomes a major limitation. It is proposed here that, based on the Target Normal Sheath Acceleration mechanism (TNSA) and the beam-target reaction scheme, the adoption of composite component target LiD as the neutron converter can be an effective path to enhance the neutron yield. Compared with the traditional LiF converter, which has two typical reaction channels p-Li and d-Li, the use of LiD converter has the advantages on introducing two more reactions channels, i.e., p-D and d-D. Therefore, more reaction channels are expected to be beneficial for increasing the neutron yield. It is experimentally demonstrated that by using LiD converter, an enhancement of 2-3 folds of neutron yield is achieved compared with the LiF converter. As a result, a neutron beam with the highest yield of 5.2×10⁸ sr^-1 with a forward beamed distribution is well obtained. The contribution of multi reaction channels is also identified, indicating the enhancement of neutron yield mainly comes from the p-D reaction.