Making Grayscale Effect using Inkscape

First just open your inkscape, then click "file" menu then choose import :

Choose your picture that you want to convert to grayscale

Then choose "filter"-->"color"-->"Desaturate" as shown below :

Then you can see that our picture has been converted to grayscale effect :

Yaaaikzzz... Just export this picture then you are done... :D
Choose "file"-->"Export Bitmap..."

For making this post more clear, please take a look to this video :