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Abstract In order to improve the accuracy and resolution for transmit beamspace (TB) multiple‐input multiple‐output (MIMO) radar, a search‐free direction‐of‐arrival (DOA) estimation method based on tensor modelling and polynomial rooting is proposed. In the proposed method, a 3‐order tensor is designed to model the received signal of TB MIMO radar on the basis of the multi‐linear property. The factor matrix with target DOA information is obtained by tensor decomposition via alternating least squares algorithm, and subsequently the DOA estimation is converted to independent minimisation of the virtual transmit beampattern for TB MIMO radar. By exploiting the Vandermonde structure of the transmit steering matrix, a polynomial function is constructed to solve the minimisation problem via polynomial rooting. The proposed method can fully take advantage of the TB technique and tensor modelling, and it requires no spectrum searching, which is different from the existing DOA estimation techniques for TB MIMO radar. The effectiveness of the proposed method is verified by simulations.