Active systems exhibit spontaneous flows induced by self-propulsion of microscopic constituents and can reach to a nonequilibrium steady state without an external drive. Constructing the analogy between the quantum anomalous Hall insulators and active matter with spontaneous flows, we show that topologically protected sound modes can arise in a steady-state active system in the continuum space. We point out that the net vorticity of the steady-state flow, which acts as a counterpart of the gauge field in condensed-matter settings, must vanish under realistic conditions for active systems. As a consequence, the quantum anomalous Hall effect naturally provides design principles for realizing topological metamaterials. We propose and analyze the concrete minimal model and numerically calculate its band structure and eigenvectors, demonstrating the emergence of nonzero bulk topological invariants with the corresponding edge sound modes. This new type of topological active systems can potentially expand possibilities for their experimental realizations and may have broad applications to practical active metamaterials. Possible realization of non-Hermitian topological phenomena in active systems is also discussed.Topologically nontrivial bands, which have been at the forefront of condensed matter physics [1][2][3][4][5][6], can also appear in various classical systems such as photonic [7-10] and phononic systems [11][12][13][14][15][16][17]. Such topologically nontrivial systems exhibit unidirectional modes that propagate along the edge of a sample and are immune to disorder. The existence of edge modes originates from the nontrivial topology characterized by bulk topological invariants of underlying photonic or acoustic band structures. The topological edge modes give rise to novel functionalities potentially applicable to, e.g., sonar detection and heat diodes [11,15]. Furthermore, they are argued to be closely related to the mechanism of robustness in biological systems [18,19].On another front, active matter, a collection of self-driven particles, has attracted much interest as an ideal platform to study biological physics [20][21][22] and out-of-equilibrium statistical physics [23][24][25][26][27][28]. While a prototype of active matter has been originally introduced to understand animal flocking behavior [29,30], recent experimental developments have allowed one to manipulate and observe artificial active systems in a controlled manner by utilizing Janus particles [31], catalytic colloids [32] and external feedback control [33].The aim of this Letter is to show that a topologically nontrivial feature can ubiquitously emerge in a nonequilibrium steady state of active matter and demonstrate it by analyzing the concrete minimal model, which can be realized with current experimental techniques. Specifically, we first point out that the net vorticity of the steady-state flow must vanish under realistic conditions for active systems in the continuum space. Since the vorticity in active matter can act as a counterpart o...