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The initial error is equal to: 0.543069
initial : 3.24471 0.0139718 1.96844 0.122383 0.00133655 1.82665 0.186222 0.716155 -0.704203 0.0360381 Exist type is: 5

The final solution is: [3.128,0.073,2.000,-0.348,0.032,1.649,0.041,0.741,-0.990,0.015]
The final error is equal to : 3571.43

After using the Levenberg-Marquardt algorithm, I got a worse answer. How could this happen? Maybe I got the jac matrix wrong? I just want to understand the reason behind it.

How do you define "error" - as "error in parameters" or "sum of squared function values"? LM performs minimization of squared sum of functions, and this metric must decrease at every step. Algorithm is designed in such way that it can not increase this metric.

From the other side - it is possible to get solution which is far away from desired one, whilst still minimizing squared sum. Say, you may have degenerate, ill-conditioned optimization problem with non-unique solution.