Experimentally observed ground state band based on the 1/2-[521] Nilsson state and the first exited band based on the 7/2-[514]Nilsson state of the odd-Z nucleus ~(255)Lr are studied by the cranked shell model(CSM) with the paring correlations treated by the particle-number-conserving(PNC) method. This is the first time the detailed theoretical investigations are performed on these rotational bands. Both experimental kinematic and dynamic moments of inertia(J~(1)and J~(2)) versus rotational frequency are reproduced quite well by the PNC-CSM calculations. By comparing the theoretical kinematic moment of inertia J~(1) with the experimental ones extracted from different spin assignments, the spin 17/2~-→13/2~- is assigned to the lowest-lying 196.6(5) ke V transition of the 1/2~-[521] band, and 15/2~-→11/2~- to the 189(1) ke V transition of the 7/2~-[514] band, respectively. The proton N = 7 major shell is included in the calculations. The intruder of the high- j low-? 1 j_((15)/2)(1/2~-[770]) orbital at the high spin leads to band-crossings at ω≈0.20( ω≈0.25) Me V for the 7/2~-[514] α =-1/2(α = +1/2) band, and at ω≈0.175 Me V for the1/2~-[521] α =-1/2 band, respectively. Further investigations show that the band-crossing frequencies are quadrupole deformation dependent. Experimentally observed ground state based on the 1 / 2- [521] Nilsson state and the first exited band based on the 7 / 2- [514] Nilsson state of the odd-Z nucleus ~ Lr are studied by the cranked shell model (CSM) with the paring correlations treated by the particle-number-conserving (PNC) method. This is the first time the detailed theoretical investigations are performed on these rotational bands. Both experimental kinematic and dynamic moments of inertia (J ~ ( 1) and J ~ (2)) versus comparing the theoretical kinematic moment of inertia J ~ (1) with the experimental ones extracted from different spin assignments, the spin 17 / 2 ~ - → 13/2 ~ - is assigned to the lowest-lying 196.6 (5) ke V transition of 1/2 ~ - [521] band, and 15/2 ~ - → 11/2 ~ The proton N = 7 major shell is included in the calculations. The intruder of the high j low-? 1 j _ ((15) / 2) (1/2 Orbital at the high spin leads to band-crossings at ω≈0.20 (ω≈0.25) Me V for the 7/2 ~ [514] α = -1/2 (α = +1/2 ) band, and at ω≈0.175 Me V for the1 / 2 ~ - [521] α = -1/2 band, respectively. Further investigations show that the band-crossing frequencies are quadrupole deformation dependent.