A method for permitting unfamiliar call, applied to a communication device having a memory and a call-blocking app to provide an unfamiliar call, includes the steps of: configuring an area in the memory of the communication device as a storage unit; recording at least one password into a password-correlated table in the storage unit, each of the at least one password being related to a specific user of the communication device; as an unfamiliar call is received, asking a caller of the unfamiliar call to provide an answer for a trivial question immediately provided by the communication device; determining whether or not the answer matches any of the at least one password in the password-correlated table; forwarding the unfamiliar call to the user corresponding to the matched password listed in the password-correlated table if positive; and, blocking the unfamiliar call if negative.