Abstract: A convex optimization based Khatri-Rao subspace wideband Direction-Of-Arrive (DOA) estimation algorithm is proposed in this paper. First of all, the steering vectors of the virtual array are formulated with the Khatri-Rao subspace. And then these steering vectors of the virtual array are used to compute the wideband focusing matrix with convex optimization. Thanks to the increased dimensions of the virtual array, the proposed focusing matrix can minimize the distortion of the noise caused by the focusing procedure and maintain the good focusing performance as well. Simulations show that the proposed method performs better than the conventional Khatri-Rao subspace wideband DOA estimation algorithm: Focusing Khatri-Rao subspace-Rotational Signal Subspace (FKR-RSS) and when the number of sources is more than the number of sensors, the proposed method has more obvious superiority especially.