Irregular fluctuation of penetration depth in CW single mode fiber laser welding is analyzed statistically and chaotically. Among various chaos theories, one of the basic concept referred as Lyapunov exponent is applied to the analysis to quantify the irregularity of penetration. Especially, maximal Lyapunov exponent (MLE) is known as the representative value indicating chaotic degree of the system dynamics. MLE calculation method of experimental data is applied to longitudinal spiking defect in fiber laser weld. Laser power modulation is suggested as a remedy then the computed MLE value is compared to CW case. It is shown that the adoption of chaos theory, MLE computation, can be used as a measurement standard to prove the validity of the solutions to prevent the unexpected chaotic behavior of weld through this work.