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In this paper, we investigate analytically the level space of the imaginarypart of quasinormal frequencies for a black hole with a deficit solid angle andquintessence-like matter by the Padmanabhan's method \cite{Padmanabhan}.Padmanabhan presented a method to study analytically the imaginary part ofquasinormal frequencies for a class of spherically symmetric spacetimesincluding Schwarzschild-de Sitter black holes which has an evenly spacedstructure. The results show that the level space of scalar and gravitationalquasinormal frequencies for this kind of black holes only depend on the surfacegravity of black-hole horizon in the range of -1 < w < -1/3, respectively . Wealso extend the range of $w$ to $w \leq -1$, the results of which are similarto that in -1 < w < -1/3 case. Particularly, a black hole with a deficit solidangle in accelerating universe will be a Schwarzschild-de Sitter black hole,fixing $w = -1$ and $\epsilon^2 = 0$. And a black hole with a deficit solidangle in the accelerating universe will be a Schwarzschild black hole,when$\rho_0 = 0$ and $\epsilon^2 = 0$. In this paper, $w$ is the parameter of stateequation, $\epsilon^2$ is a parameter relating to a deficit solid angle and$\rho_0$ is the density of static spherically symmetrical quintessence-likematter at $r = 1$.

A simple derivation of level spacing of quasinormal frequencies for a black hole with a deficit solid angle and quintessence-like matter