As the fourth synchrotron radiation light source, diffraction-limited storage rings (DLSRs) are being vigorously developed and constructed around the world. How to efficiently inject beam into the storage ring while minimizing the disturbance to the stored beam is one of the important issues in the design and operation of DLSRs. The conventional bump injection which has a long history is widely used and has mature technology. However, it disturbs the stored beam and the small dynamic aperture of DLSRs, which makes it difficult to apply the conventional bump injection on DLSRs. To solve these problems, some conventional off-axis injection method have been improved and several on-axis injection methods have been proposed and developed. Hefei Advanced Light Facility (HALF) is a DLSR under planning and construction. Based on the physical design of the HALF storage ring, a couple of off-axis or on-axis injection schemes have been designed and applied. Their feasibility has been verified through particle tracking and simulation, and physical issues such as injection efficiency have been studied. Discussion of results and conclusion are also presented.