I would like to use ARIMA model to forecast next steps in time series. Unfortunately because of increasing variance data is non-stationary. Is there any way to transform my data to get rid of this variance? In addition before training I normalised data. Is normalisation required by ARIMA model?
As Demetrios says, you could try transforming your data to stabilize the variance. The classical approach is to use a Box-Cox transformation. One special case of this is the log transform. Some software will estimate a Box-Cox transformation parameter $\lambda$ for you.
Alternatively, as mlofton says, you could consider modeling your variance directly using an ARCH or a GARCH model. Your data does look somewhat like a financial returns series to me, with an essentially constant mean. In finance, we are often most interested in modeling variances, not so much means, and ARCH/GARCH is custom-made for this.