We propose a new concept of gravity gradiometer, GREMLIT, for the determination of the spatial derivatives of gravitational acceleration during airborne surveys. The core of this instrument is the acceleration gradiometer composed of four ultra-sensitive electrostatic planar accelerometers, inheriting from technologies developed for the GRACE and GOCE satellite gravity missions. Data from these missions have greatly improved our knowledge of the Earth’s gravity field and its time variations. However, resolving wavelengths of a few 10 km or less, beyond the reach of the satellite resolution, is of utmost importance to study a number of crustal geophysical processes and geological structures. We first present the benefits for a new gravity gradiometer, then we describe the planar acceleration gradiometer, which put together with three orthogonal gyroscopes, constitutes the gravity gradiometer GREMLIT. The acceleration gradiometer enables measurement at one point of the horizontal spatial derivatives of the acceleration horizontal components. We explain the measurement principle and describe the computation of the gravity gradients along with the necessary ancillary measurements. From a detailed error budget analysis of the accelerometers, an expected spectral sensitivity below \text{1E/}\sqrt{\text{Hz}} is found in the [10^-3, 0.2] Hz measurement bandwidth. To maintain such performance in flight, we finally discuss the adaptation of the acceleration gradiometer to the turbulent airborne environment. To limit the saturation of the accelerometers, we propose to cancel the common-mode output of the acceleration gradiometer by integrating the instrument on a double-gimbal platform controlled by the common-mode. We demonstrate on a real case study that with such a solution, it is technically possible to prevent the saturation of the accelerometers at least 95% of the time and it is not damaging to the airborne survey.