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In this paper we prove that, under certain conditions, a strong law of largenumbers holds for a class of super-diffusions $X$ corresponding to theevolution equation $\partial_t u_t=L u_t+\beta u_t-\psi(u_t)$ on a boundeddomain $D$ in $\R^d$, where $L$ is the generator of the underlying diffusionand the branching mechanism  $\psi(x,\lambda)=1/2\alpha(x)\lambda^2+\int_0^\infty (e^{-\lambdar}-1+\lambda r)n(x, {\rm d}r)$ satisfies $\sup_{x\in D}\int_0^\infty (r\wedger^2) n(x,{\rm d}r)<\infty$.

Strong law of large number of a class of super-diffusions