<p>In this paper, a combination solution method based on the analogy of the generalized-<i>α</i> (AG-<i>α</i>) method is proposed to solve linear rigid-flexible coupling structural dynamic problems, which is termed the G-G(<i>ρ</i>_1∞, <i>ρ</i>_2∞) combination solution method. In the G-G(<i>ρ</i>_1∞, <i>ρ</i>_2∞) method, the degrees of freedom of the system are divided into two groups. One group with larger stiffness is solved by using the AG-<i>α</i> method with parameters determined by the spectral radius <i>ρ</i>_1∞ corresponding to the infinite frequency. The other, with smaller stiffness, is solved by using the AG-<i>α</i> method with parameters determined by <i>ρ</i>_2∞. Taking two differential equations of second order as test equations, the amplification matrix of the G-G(<i>ρ</i>_1∞, <i>ρ</i>_2∞) method has two pairs of principal eigenvalues and two spurious eigenvalues. The percentage amplitude decay and period elongation are defined and investigated with the two algorithmic frequencies and two algorithmic damping ratios. In addition, the accuracy order and stability of the combination method are discussed. Numerical examples show that the G-G(<i>ρ</i>_1∞, <i>ρ</i>_2∞) method can filter out the high-frequency modes and simultaneously keep the low-frequency modes when solving rigid-flexible coupling structural dynamic problems, and its numerical performances are superior to the AG-<i>α</i> method.</p>