Bit allocation or quantizer assigning problem is a basic and essential issue in lossy picture coding. It could be represented as minimizing overall distortion with the given constraint that total bits should not exceed allowed bit-budget. Optimal solution can be found by Lagrangian method. However this method needs much computational time and memory. This paper presents an approximation method that uses the activity measure. The comparison between the existing activity measuring techniques are made, and mapping function from activity value to the quantizer is proposed. Under MPEG-1 Intra coding situation, simulations show almost identical results compared to the optimal ones obtained by Lagrangian method with reduced computational time.