Cloud computing has changed the way enterprises store, access and share data. Data is constantly being uploaded to the cloud and shared within an organization built on a hierarchy of many different individuals that are given certain data access privileges. With more data storage needs turning over to the cloud, finding a secure and efficient data access structure has become a major research issue. With different access privileges, individuals with more privileges (at higher levels of the hierarchy) are granted access to more sensitive data than those with fewer privileges (at lower levels of the hierarchy). In this paper, a Privilege-based Multilevel Organizational Data-sharing scheme~(P-MOD) is proposed that incorporates a privilege-based access structure into an attribute-based encryption mechanism to handle these concerns. Each level of the privilege-based access structure is affiliated with an access policy that is uniquely defined by specific attributes. Data is then encrypted under each access policy at every level to grant access to specific data users based on their data access privileges. An individual ranked at a certain level can decrypt the ciphertext (at that specific level) if and only if that individual owns a correct set of attributes that can satisfy the access policy of that level. The user may also decrypt the ciphertexts at the lower levels with respect to the user's level. Security analysis shows that P-MOD is secure against adaptively chosen plaintext attack assuming the DBDH assumption holds.The comprehensive performance analysis demonstrates that P-MOD is more efficient in computational complexity and storage space than the existing schemes in secure data sharing within an organization.