We demonstrate carbon nanotube (CNT) composite-based optoacoustic transmitters that generate strong and high frequency ultrasound. The composite consists of CNTs grown on a substrate, which are embedded in elastomeric polymer used as an acoustic transfer medium. Under pulsed laser excitation, the composite generates very strong optoacoustic pressure: 18 times stronger than a Cr film reference and five times stronger than a gold nanoparticle composite with the same polymer. This enhancement persists over a broadband frequency range of up to 120 MHz and is confirmed by calculation. We suggest the CNT-polymer composites as highly efficient optoacoustic transmitters for high resolution ultrasound imaging.