In multi-beam satellite system, dynamically adjusting the beams to meet the communication demands of ground users, adapt to changes in user distribution, and consider satellite hardware limitations is a technological challenge. To end this, this paper proposes an adaptive beamwidth design scheme. The scheme utilizes an enhanced K-means (called eK-means) clustering algorithm for user grouping and assigns suitable beams to each group, ensuring that all users within the same group are positioned within the primary radiation region of the beam. Also, a greedy frequency allocation strategy is introduced to mitigate inter-group interference. Given its capacity to dynamically tailor the number and coverage of beams based on user distribution and demands of communication, the proposed scheme greatly bolsters the flexibility of multi-beam satellite systems. Simulation results showcase its exceptional performance.