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In a (t, n) threshold proxy signature scheme, the original signer delegates the power of signing messages to a designated proxy group of n members. Any t or more proxy signers of the group can cooperatively issue a proxy signature on behalf of the original signer, but (t - 1) or less proxy signers cannot. Previously, all of the proposed threshold proxy signature schemes have been based on the discrete logarithm problem and do not satisfy all proxy requirements. In this paper, we propose a practical, efficient, and secure (t, n) threshold proxy signature scheme based on the RSA cryptosystem. Our scheme satisfies all proxy requirements and uses only a simple Lagrange formula to share the proxy signature key. Furthermore, our scheme requires only 5 percent of the computational overhead and 8 percent of the communicational overhead required in Kim's scheme.