- My current goal is to improve my skills in English.
I’m not sure and little bit puzzled whether the grammar construction of the sentence works like that and the sentence sounds natural.
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Yes, it's grammatically correct. You can also say:
My current goal is to improve my English skills.
My current goal is to improve my skills in English.
is grammatically correct. If you explain what makes you feel uncomfortable with it, we can provide you with more details.