  In this paper, we present a black hole solution with a cosmological constant
in the Scalar-Tensor-Vector Modified Gravity (MOG) theory, where the strength
of the gravitational constant is determined by $G = G_\text{N}(1+\alpha)$. We
derive the master equations for gravito-electromagnetic perturbations and
numerically solve for the Quasinormal Mode (QNM) spectrum and the ringdown
waveforms. Our research results show that increasing the MOG parameter $\alpha$
leads to a decrease in both the real and imaginary parts of the QNM frequencies
for electromagnetic and gravitational modes. Similarly, increasing the
cosmological constant $\Lambda$ also results in a decrease in both the real and
imaginary parts of the QNM frequencies for these modes. These trends are
observed when compared to standard Schwarzschild-de Sitter (S-dS) or MOG black
holes, respectively. Meanwhile, the result indicates that in the MOG-de Sitter
spacetime, the frequencies for electromagnetic and gravitational modes display
isospectrality, and exhibit the same ringdown waveforms. Our findings have
implications for the ringdown phase of mergers involving massive compact
objects, which is of particular relevance given the recent detections of
gravitational waves by LIGO.
