Alginate lyases show great potential for industrial and medicinal applications, especially as an attractive biocatalyst for the production of oligosaccharides with special bioactivities. A novel alginate lyase, AlyH1, from the marine bacterium Vibrio furnissii H1, which has been newly isolated from rotten seaweed, was purified and characterized. The purified enzyme showed the specific activity of 2.40 U/mg. Its molecular mass was 35.8 kDa. The optimal temperature and pH were 40 °C and pH 7.5, respectively. AlyH1 maintained stability at neutral pH (7.0–8.0) and temperatures below 30 °C. Metal ions Na+, Mg2+, and K+ increased the activity of the enzyme. With sodium alginate as the substrate, the Km and Vmax values of AlyH1 were 2.28 mg/mL and 2.81 U/mg, respectively. AlyH1 exhibited activities towards both polyguluronate and polymannuronate, and preferentially degraded polyguluronate. Products prepared from sodium alginate by AlyH1 were displayed to be di-, tri-, and tetra-alginate oligosaccharides. A partial amino acid sequence (190 aa) of AlyH1 analysis suggested that AlyH1 was an alginate lyase of polysaccharide lyase family 7. The sequence showed less than 77% identity to the reported alginate lyases. These data demonstrated that AlyH1 could be as a novel and potential candidate in application of alginate oligosaccharides production with low polymerization degrees.