In AsiaCCS 2011, Wang \textit{et al.} proposed a two-level heuristic
sieve algorithm for the shortest vector problem in lattices, which
improves the Nguyen-Vidick sieve algorithm. Inspired by their idea, we
present a three-level sieve algorithm in this paper, which
is shown to have better time complexity. More precisely, the time complexity of our algorithm is
$2^{0.3778n+o(n)}$ polynomial-time operations and the corresponding space complexity is
$2^{0.2833n+o(n)}$ polynomially many bits.
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