The weighted visual cryptographic scheme (WVCS) is a secret sharing technology, where weights are assigned to each shadow (participant) according to its importance. Among WVCS, the random grid-based WVCS (RGWVCS) is a frequently visited subject. It considers the premise of equality of all participants, without taking into account the existence of privileged people in reality. To address this problem of RGWVCS, this paper designs a new model, named as (k, m, n)-RGWVCS (where
m
<
k
<
n
), in which the secret is encrypted into n shares and sent to k participants. In the recovery end, the secret could be reconstructed by minimum m shares when the privileged join in; otherwise, k shares are needed. The experimental results show that our method has the advantage of no pixel expansion and no codebook design by means of random grid. Moreover, the contrast of our model increased by 32.85% on average compared with that of other WVCS.