Relu with not gradient vanishing function is possible?
If you are using an activation like y=x, then your model is a simple linear one. Multiple layers with such activation will be equivalent/reduced to only one layer with a linear activation! Thus you can only map linear function satisfactorily with this type of model. To be able to learn complex non-linear functions, you need to use multiple layers with non-linear activation in between to make the whole model non-linear 

To prevent the vanishing gradient problem, there is a variant of relu called Leaky ReLU. This activation is same as relu in the positive region of x. For negative region of x, it is a linear function with a small slope (e.g. 0.2). This makes Leaky ReLU a non linear activation at x=0 point.