It is highly desirable for designing ferroelectric heterostructure that is capable of harnessing wide-range solar spectrum and efficiently separating photocarriers by a combination of narrow bandgap semiconductors in other systems. Single-wall carbon nanotubes (SWCNTs) have been utilized good building blocks for photovoltaic applications, because of their strong wide range (ultraviolet to infrared)-light absorption and excellent physical properties (i.e., direct bandgap, an electronic sub-band structure, and high carrier mobility). Herein, we demonstrate high-performance ferroelectric photovoltaic heterostructures comprised of semiconducting SWCNTs as a p-type layer and ferroelectric BiFeO3 (BFO) thin films on n-type single crystal Nb doped SrTiO3 (Nb:STO) substrate. Their Voc and Jsc reached up to 0.21 V and 1.95 mA cm-2, respectively, which are larger than those of single structure of BFO/Nb:STO. In addition, SWCNT/BFO heterostructures exhibited tunable photovoltaic effect by controlling electric polarization, which is useful for optoelectronic devices including optical sensors, solar cells, and photovoltaic readable nonvolatile memories.