Summary: This article studies the limiting spectral distributions of random birth-death \(Q\) matrices. Under the strictly stationary ergodic condition, we prove that the empirical spectral distribution converges weakly to a nonrandom probability distribution. Furthermore, in the situations without strictly stationary ergodic condition, we study a class of random birth-death \(Q\) matrices corresponding to generalizations of the Beta-Hermite ensembles, and establish the existence as well as convolution formulations for their limiting spectral distributions. In particular, for the random birth-death \(Q\) matrices corresponding to the Beta-Hermite ensembles, the limiting spectral distribution is the convolution of the semi-circle law and Dirac measure \(\delta_{-2}\).