A low-stress packaging structure for a MEMS acceleration sensor chip includes a MEMS sensor chip and a chip carrier. Two sides of the bottom of the sensor chip are provided with a first metal layer and a second metal layer respectively. Two sides of a die attach area of the chip carrier are correspondingly provided with a third metal layer and a fourth metal layer. The first metal layer of the sensor chip and the third metal layer of the chip carrier are bonded together. The second metal layer of the sensor chip and the fourth metal layer of the chip carrier are only in contact but not bonded. A groove is arranged between the first metal layer and the second metal layer at the bottom of the sensor chip. A certain gap is defined between the sensor chip and cavity walls of chip carrier.