A hierarchical threshold scheme is a scheme to solve the secret sharing with a hierarchical access structure where participants are partitioned into different levels. In the past hierarchical threshold scheme participants are partitioned based on a single attribute. But in practice, each participant always has several attributes, and the group of participants always should be partitioned based on different attributes to satisfy the security requirements. For example, Distinguished by position, the bank employees can be tellers or department managers. Distinguished by department, the bank employees can be from account department, administration department or others. The bank policy could require the presence of 5 employees in opening the vault, at least one of whom must be department manager, and at least 3 of whom are from account department. Even though hierarchical threshold scheme has been studied extensively in the past, none of the existing solutions solves the above problem. We propose a multi-attribute hierarchical threshold scheme based on Tassa's scheme, which is based on Birkhoff interpolation, and Mignotte's scheme, which is based on Chinese Remainder Theorem, to solve this problem.