<p>In this paper, we focus on peaked traveling wave solutions of the modified highly nonlinear Novikov equation by dynamical systems approach. We obtain a traveling wave system which is a singular planar dynamical system with three singular straight lines, and derive all possible phase portraits under corresponding parameter conditions. Then we show the existence and dynamics of two types of peaked traveling wave solutions including peakons and periodic cusp wave solutions. The exact explicit expressions of two peakons are given. Besides, we also derive smooth solitary wave solutions, periodic wave solutions, compacton solutions, and kink-like (antikink-like) solutions. Numerical simulations are further performed to verify the correctness of the results. Most importantly, peakons and periodic cusp wave solutions are newly found for the equation, which extends the previous results.</p>