Periodic and solitary wave solutions are investigated numerically for a perturbed Korteweg–de Vries equation with unstable and dissipation terms in Hilbert transform: u t+uu x+u xxx+η( Hu x+ Hu xxx)=0 . A family of solitary wave solutions S (1), S (2),…, S ( n) ,…, whose members are distinguished by the number of “humps”, is numerically identified. The tails of these waves decay as O(1/∣ x∣ 2) when ∣ x∣→∞ irrespective of the magnitude of η. It is also found that for a given η, there exist families of periodic wave solutions P (1), P (2),…, P ( n) ,…, which originate from one near-sinusoidal wave and end up in the infinite periodicity to the corresponding solitary waves. The numerical results are consistent with the theoretical estimates based on the conservation properties.