In an incomplete market it is usually impossible to eliminate the intrinsic risk of an option. In this case, quadratic-risk minimization is often used to determine a hedging strategy. However, it may be more natural to use piecewise linear risk-minimization. We investigate hedging strategies using piecewise linear risk-minimization. We illustrate that this criterion for risk-minimization may lead to smaller expected total hedging cost and significantly different, possibly more desirable, hedging strategies from those of quadratic risk-minimization. The distributions of the total hedging cost and risk show that hedging strategies obtained by piecewise linear risk-minimization have a larger probability of small cost and risk, though they also have a very small probability of larger cost and risk. Comparative numerical results are provided. We also prove that the value processes of these hedging strategies satisfy put-call parity.