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In algebraic geometry, superspecial curves are important research objects.While the number of superspecial genus-3 curves in characteristic $p$ is known,the number of hyperelliptic ones among them has not been determined even forsmall $p$. In this paper, in order to compute the latter number, we give analgorithm for computing the $(2,2,2)$-isogeny graph of superspecial abelianthreefolds by using theta functions. This enables us to list up allsuperspecial genus-3 curves efficiently. Executing this algorithm on Magma, wesucceeded in counting all superspecial hyperelliptic curves of genus $3$ when$11 \leq p < 100$, and in finding a single one when $7 \leq p < 10000$.

Computing Richelot isogeny graph of superspecial abelian threefolds