The present invention provides a single shell-pass shell-and-tube heat exchanger with helical baffles, where within a single pitch, the helical baffles are separated into inner and outer parts along the radial direction of the shell. In the central portion of the inner space of the shell, an inner non-continuous helical form is employed; in other portion outside the central portion, doughnut shaped helical baffles with continuous curved surfaces are arranged to form an outer continuous helical baffle, and the outer helical baffles are arranged to surround the inner helical baffles. Furthermore, the present invention relates to a multiple shell-pass shell-and-tube heat exchanger with helical baffles, in which complete continuous helical baffles are provided in shell-sides other than the inner shell-pass, while non-continuous helical baffles or other flow guide means are employed in the inner shell-pass. The present invention makes flow patterns of fluids on the shell side more desirable, leading to a reduced flow pressure drop, and mitigate fouling, thus the heat transfer rate is improved and the service life of the heat exchanger is increased. The present invention also provides two methods for manufacture of continuous helical baffles, which ensure the concentricity of the tube bundle holes on each continuous helical baffle so as to facilitate installation of heat exchange tube bundles.