In this letter, we consider one-to-all broadcast on distributed memory parallel computers based on message-passing, such as cluster of WSs or PCs. We present an efficient broadcast algorithm, called overlapped-two-phase broadcast (O2PB), that is an enhanced version of two-phase broadcast (2PB). The O2PB algorithm is compared with other algorithms, such as linear broadcast, tree broadcast and 2PB algorithms. According to our theoretical and experimental results, when the size of message to be broadcasted is large, the O2PB algorithm is fastest among all the algorithms. The O2PB algorithm is approximately 20% faster than the 2PB algorithm.