Conditions for the excitation of Alfvén eigenmodes (AEs) by energetic ions are investigated in neutral-beam-injection (NBI) heated plasmas of the Large Helical Device (LHD). This study is carried out in a wide parameter range of the beta values of the energetic ion components and the ratio of the energetic ion velocity to the Alfvén velocity (up to with the assumption of classical slowing down and ). These ranges of parameters cover those predicted for the International Thermonuclear Experimental Reactor (ITER). During this experimental campaign of LHD, toroidicity-induced AEs (TAEs) with n = 1–5 (n being the toroidal mode number), global AEs (GAEs) with n = 0 and 1, and energetic particle modes (EPMs) were observed. The effect of the magnetic configuration on the TAE spectrum was also investigated. In magnetic configurations with relatively high magnetic shear, only TAEs with n = 1 and 2 were observed. On the other hand, TAEs with n up to 5 were observed in magnetic configurations with low magnetic shear. For two typical shots obtained in magnetic configurations characterized by different values of the magnetic shear, eigenfunctions of TAEs were calculated by using a global mode analysis code CAS3D3. The calculated results indicate that the eigenfunctions tend to be localized around the relevant TAE gaps. When the gap is located in the plasma core region (normalized minor radius ρ ⩽ 0.4), the TAE tends to become a core-localized type. When the gap is in the outer region (typically 0.5 ⩽ ρ ⩽ 0.9) of the plasma, the TAE tends to (a) either become a global type having a radially extended structure if the magnetic shear is very weak in the core region inside the gap, (b) or become a gap localized type in the case of finite central magnetic shear. Transition of the eigenmode from the core-localized type with m ∼2/n = 1 TAEs (m being the poloidal mode number) to the n = 1 GAEs (or cylindrical AEs) has been observed when the rotational transform at the core ι (0)/2π exceeds the specific value of ι(0)/2π = 0.4.