In this paper, direction-of-arrival estimation using nested array is studied in the framework of sparse signal representation. With the vectorization operator, a new real-valued nonnegative sparse signal recovery model which has a wider virtual array aperture is built. To leverage celebrated compressive sensing algorithms, the continuous parameter space has to be discretized to a number of fixed grid points, which inevitably incurs modeling error caused by off-grid gap. To remedy this issue, a block alternating optimization method is put forth that jointly estimates the sparse signal and refines the locations of grid points. Specifically, inspired by the majorization minimization, the proposed method iteratively minimizes a surrogate function majorizing the given objective function, where only a single block of variables are updated per iteration while the remaining ones are kept fixed. The proposed method features affordable computational complexity, and numerical tests corroborate its superior performance relative to existing alternatives in both overdetermined and underdetermined scenarios.