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In this paper, we study the symmetric travelling wave solutions of the <i>b</i>-family of the Novikov equation. We show that the <i>b</i>-family of the Novikov equation can provide symmetric travelling wave solutions, such as peakon, kink and smooth soliton solutions. In particular, the single peakon, two-peakon, stationary kink, anti-kink, two-kink, two-anti-kink, bell-shape soliton and hat-shape soliton solutions are presented in an explicit formula.