网上找到的答案一般是需要再装一个安装包，但libcurl4-gnutls-dev或libcurl4-openssl-dev都不适用于我的CentOS 6。

我的情况是：

$ yum search curl
Loaded plugins: security
======================================== N/S Matched: curl =========================================
asterisk-curl.x86_64 : Modules for Asterisk that use cURL
curlftpfs.x86_64 : CurlFtpFS is a filesystem for accessing FTP hosts based on FUSE and libcurl
curlpp.i686 : A C++ wrapper for libcURL
curlpp.x86_64 : A C++ wrapper for libcURL
curlpp-devel.i686 : Development files for curlpp
curlpp-devel.x86_64 : Development files for curlpp
libcurl-devel.i686 : Files needed for building applications with libcurl
libcurl-devel.x86_64 : Files needed for building applications with libcurl
ocaml-curl.x86_64 : OCaml Curl library (ocurl)
ocaml-curl-devel.i686 : Development files for ocaml-curl
ocaml-curl-devel.x86_64 : Development files for ocaml-curl
perl-WWW-Curl.x86_64 : Perl extension interface for libcurl
php-pear-Net-Curl.noarch : OO interface to PHP's cURL extension
python-pycurl.x86_64 : A Python interface to libcurl
python34-pycurl.x86_64 : Python interface to libcurl for Python 3
uwsgi-alarm-curl.x86_64 : uWSGI - Curl alarm plugin
uwsgi-plugin-curl-cron.x86_64 : uWSGI - Plugin for CURL Cron support
curl.x86_64 : A utility for getting files from remote servers (FTP, HTTP, and others)
libcurl.i686 : A library for getting files from web servers
libcurl.x86_64 : A library for getting files from web servers
rubygem-curb.x86_64 : Ruby libcurl bindings
uwsgi-alarm-xmpp.x86_64 : uWSGI - Curl alarm plugin

  Name and summary matches only, use "search all" for everything.

直觉告诉我是需要这个libcurl-devel

于是装之，然后就能够pip install pycurl了。