A support capable of fully-automatically performing transverse clamping by means of single gear linkage comprises a back side base (10), and comprises a bottom supporting arm (20), a left-side gripping arm (30) and a right-side gripping arm (40) mounted on the back side base. A return elastic member (50) is fixedly mounted relative to the back side base. A travel slot (23) extending in a vertical direction is formed in the bottom supporting arm, and a vertical spur rack portion (24) is disposed on the inner side of the travel slot. A gear (60) extending back and forth is fixedly disposed relative to the back side base, and engages with the vertical spur rack portion. Each of the left-side gripping arm and the right-side gripping arm is provided with a transverse spur rack portion (41), and the two transverse spur rack portions respectively engage with the top and the bottom of the gear. Accordingly, when a mobile device such as a mobile phone is placed, the bottom supporting arm is pressed to downwards move due to the gravity of the mobile phone, and at the same time, and the left-side gripping arm and the right-side gripping arm inwards and transversely move to automatically and tightly clamp the mobile phone; when the mobile phone is taken out, the bottom supporting arm upwards moves under the return acting force of the return elastic member, and at the same time, in a linked manner, the left-side gripping arm and the right-side gripping arm outwards and transversely move to automatically release the mobile phone.