Broadcast encryption (BE) is an effective method to broadcast encrypted confidential content, although it does not support the transmission of personalized messages to individuals. Broadcast encryption with personalized messages (BEPM) simultaneously transmits not only the common encrypted message to a group of users but also encrypted personalized messages to individual users. Currently available BEPM schemes fail to provide the recipient’s anonymity that means the information of the subscriber set is available to the enemies. This paper first introduces a new BEPM paradigm, called identity-based outsider anonymous broadcast encryption with personalized messages (IB-OAnoBEPM), by tweaking the identity-based framework over the most advanced and secure asymmetric Type-3 variant of the bilinear maps. In addition to being adaptively secure, our construction withstands indistinguishable chosen-plaintext attack under the standard asymmetric decisional bilinear Diffie-Hellman exponent assumption without using the random oracle model. More positively, the proposed scheme is the first BEPM system that achieves security without any non-standard q-type assumptions. In particular, our design is very efficient both in terms of communication and computation costs, as the ciphertext size is constant, and the decryption algorithm requires only three asymmetric bilinear pairings to recover the correct message and the personalized messages, which are highly desirable for light-weight devices.