Operation characteristics of tapered-waveguide traveling wave semiconductor laser amplifier (TTW-SLA) are calculated in terms of quasi adiabatic single mode propagation, signal gain and saturation output power, device efficiency(the efficiency of conversion between the electrical and amplified optical power), and amplified spontaneous emission (ASE) power, and their dependences on the shape of the taper are compared for linear, quadratic, Gaussian and exponential functions, It was found that in the allowed quasi adiabatic single mode propagation condition, linear and Gaussian TTW-SLA have higher saturation output power property, while the exponential TTW-SLA has higher device efficiency property and lower ASE noise of about 0.1 times that of a broad type TW-SLA.