We theoretically propose a temporal cloaking scheme based on accelerating wave packets. A part of a monochromatic lightwave is endowed with a discontinuous nonlinear frequency chirp, so that two opposite accelerating caustics are created in space-time as the different frequency components propagate in the presence of dispersion. The light intensity in the interior of this biconvex time gap is negligible, thus concealing the enclosed events. In contrast to previous temporal cloaking schemes,

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... e light propagates successively through two different media with opposite dispersions, accelerating wave packets open and close the cloaked time window continuously in a single dispersive medium. In addition, biconvex time gaps can be tailored into arbitrary shapes and offer a larger suppression of intensity compared to their rhombic counterparts.