The current paper is devoted to random dynamics of stochastic partly dissipative systems perturbed by Lévy noise. By the technique of dissipative in probability and multivalued random dynamical systems (MRDS), the existences of random attractor for MRDS generated by the stochastically perturbed partly dissipative systems are provided, both the weaker restrictions and stronger restrictions on the coefficients of Lévy noise respectively. Mathematics Subject Classification: 35R60; 60H15; 35K57.

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... words: multivalued random dynamical systems, random attractor, dissipative in probability, Lévy noise (1:1) where a > 0, Q ⊂ R n is a bounded domain with smooth boundary, f, g C(R), h L 2 (Q), f and g satisfy some appropriate assumptions, and h(t, ω) is a stochastic càdlag process with right continuity and left limits.