An off-grid direction-of-arrival (DOA) estimation method based on block sparse representation is proposed to localize the strictly noncircular (NC) sources utilizing an extended transformed nested array (ETNA). This novel off-grid DOA estimation algorithm effectively promotes spatial distribution information mining. Furthermore, it is conducive to providing stable signal recovery, which refines the DOA estimation precision with interpolation over a coarse grid. We then combine the above algorithm with the designed ETNA to improve the detection performance. The ETNA is an optimal displacement on the existing TNA, which enlarges the degree of freedom (DOF) and lengthens the maximum contiguous segment from the derived virtual array. Simulation results demonstrate its superiority in estimation performance and DOF.