I installed R 4.0.3 and Rstudio. Then I installed BiocManager by the following command.

Operation:

if (!requireNamespace("BiocManager", quietly = TRUE))
    install.packages("BiocManager")
BiocManager::install(version="3.11")

The response:

Bioconductor version 3.11 (BiocManager 1.30.10), R 4.0.3 (2020-10-10)

So it seems ok.

But I CAN'T succeed to install GEOquery.

Operation:

BiocManager::install("GEOquery" ) 

Responses:

URL’https://mirrors.ustc.edu.cn/CRAN/bin/windows/contrib/4.0/curl_4.3.zip'
Content type 'application/zip' length 4126745 bytes (3.9 MB)
downloaded 3.9 MB
......
URL’https://bioconductor.org/packages/3.11/bioc/bin/windows/contrib/4.0/GEOquery_2.56.0.zip'
Content type 'application/zip' length 13932568 bytes (13.3 MB)
downloaded 164 KB

Error in read.dcf(file.path(pkgname, "DESCRIPTION"), c("Package", "Type")) : 
Cann't open the link.
Warning messages:
1: In download.file(url, destfile, method, mode = "wb", ...) :
  downloaded length 536576 != reported length 746705
2: In download.file(url, destfile, method, mode = "wb", ...) :
  downloaded length 442368 != reported length 2418713
3: In download.file(url, destfile, method, mode = "wb", ...) :
  downloaded length 49152 != reported length 3167021
4: In download.file(url, destfile, method, mode = "wb", ...) :
  downloaded length 167936 != reported length 13932568
5: In unzip(zipname, exdir = dest) : Error in extracting 1  from zip file.
6: In read.dcf(file.path(pkgname, "DESCRIPTION"), c("Package", "Type")) :
  Can't open the compressed file 'BiocGenerics/DESCRIPTION'，Possible due to 'No such file or directory'

It seems something wrong is with BiocGeneric.

Could anyone help me? Thank you in advance. I spent a few hours on it but just cann't solve it.

This looks like a download issue. I can't reproduce the error with Bioconductor 3.11 installing GEOquery and BiocGenerics. I would suggest you try again.