A vehicle battery diagnosis apparatus includes: a measurement unit configured to measure a battery cell voltage; and a controller configured to diagnose a cell voltage deviation based on the battery cell voltage. The controller calculates a self-discharge rate for each cell based on the battery cell voltage and a parking time and calculates the cell voltage deviation based on the battery cell voltage, and when the calculated cell voltage deviation is greater than a preset cell balancing reference voltage deviation, the controller compares cell balancing capacitance calculated based on a vehicle usage time with a maximum self-discharge rate among the calculated self-discharge rates for respective cells and determines whether cell balancing is enabled or diagnoses the cell voltage deviation.